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Ramakrishnan} } @Article{ gordon:dlp, author = {Gordon, D.}, year = {2004}, title = {Discrete Logarithm Problem, \hfill\\ {\tt http://www.win.tue.nl/\~{ }henkvt/Content.html}} } @Proceedings{ mr98i:94002, title = {Advances in cryptology---{EUROCRYPT} '97}, series = {Lecture Notes in Computer Science}, volume = {1233}, booktitle = {Proceedings of the 16th International Conference on the Theory and Application of Cryptographic Techniques held in Konstanz, May 11--15, 1997}, editor = {Fumy, Walter}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1997}, pages = {xii+509}, isbn = {3-540-62975-0}, mrclass = {94-06 (68P25 94A60)}, mrnumber = {98i:94002} } @Article{ nechaev:lower, author = {Nechaev, V. I.}, title = {On the complexity of a deterministic algorithm for a discrete logarithm}, journal = {Mat. Zametki}, fjournal = {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki}, volume = {55}, year = {1994}, number = {2}, pages = {91--101, 189}, issn = {0025-567X}, mrclass = {11Y16}, mrnumber = {96a:11145} } @InCollection{ shoup:lower, author = {Shoup, Victor}, title = {Lower bounds for discrete logarithms and related problems}, booktitle = {Advances in cryptology---EUROCRYPT '97 (Konstanz)}, series = {Lecture Notes in Comput. Sci.}, volume = {1233}, pages = {256--266}, publisher = {Springer}, address = {Berlin}, year = {1997}, mrclass = {94A60 (68P25 68Q25)}, mrnumber = {98j:94023} } @Article{ gordon:dlog, author = {Gordon, Daniel M.}, title = {Discrete logarithms in {${\rm GF}(p)$} using the number field sieve}, journal = {SIAM J. Discrete Math.}, fjournal = {SIAM Journal on Discrete Mathematics}, volume = {6}, year = {1993}, number = {1}, pages = {124--138}, issn = {0895-4801}, coden = {SJDMEC}, mrclass = {11Y16 (11N36)}, mrnumber = {94d:11104}, mrreviewer = {Joe P. Buhler} } @Article{ python, author = {Rossum, Guido van}, title = {Python,\newline{\tt http://www.python.org}} } @article{ cha:vanishing, author = {Cha, Byungchul}, title = {Vanishing of some cohomology groups and bounds for the {S}hafarevich-{T}ate groups of elliptic curves}, journal = {J. Number Theory.}, year = {2005}, volume = {111}, issue = {1}, pages = {154--178}, date = {March 2005} } @Article{ cha:shabound, author = {Cha, Byungchul}, title = {Vanishing of {S}ome {C}ohomology {G}roups and {B}ounds for the {S}hafarevich-{T}ate {G}roups of {E}lliptic {C}urves}, journal = {Johns-Hopkins Ph.D. Thesis}, year = {2003} } @Article{ cassels:7, author = {Cassels, J. W. S.}, title = {Arithmetic on curves of genus 1. {VIII}. {O}n conjectures of {B}irch and {S}winnerton-{D}yer}, journal = {J. Reine Angew. Math.}, volume = {217}, year = {1965}, pages = {180--199}, mrclass = {14.48 (14.49)}, mrnumber = {31 \#3420}, mrreviewer = {T. Ono} } @Article{ kedlaya:counting-errata, author = {Kedlaya, K.\thinspace{}S.}, title = {Errata for: ``{C}ounting points on hyperelliptic curves using {M}onsky-{W}ashnitzer cohomology'' [{J}. {R}amanujan {M}ath.\ {S}oc.\ {\bf 16} (2001), no. 4, 323--338}, note = {Dedicated to Professor K. S. Padmanabhan}, journal = {J. Ramanujan Math. Soc.}, fjournal = {Journal of the Ramanujan Mathematical Society}, volume = {18}, year = {2003}, number = {4}, pages = {417--418}, issn = {0970-1249}, mrclass = {14G05 (11G25 14F43 14G15)}, mrnumber = {2 043 934} } @Article{ abbott:padic, author = {Abbott, J.}, title = {Recovery of algebraic numbers from their $p$-adic approximations}, journal = {Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation}, pages = {112--120}, year = {1989}, isbn = {0-89791-325-6}, publisher = {ACM Press, New York, NY, USA} } @Article{ tate:arithmetic, author = {Tate, J.}, title = {The arithmetic of elliptic curves}, journal = {Invent. Math.}, volume = {23}, year = {1974}, pages = {179--206}, mrclass = {10D05 (14G25 14K15)}, mrnumber = {54 \#7380}, mrreviewer = {A. P. Ogg} } @Article{ mazur-tate:sigma, author = {Mazur, B. and Tate, J.}, title = {The {$p$}-adic sigma function}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {62}, year = {1991}, number = {3}, pages = {663--688}, issn = {0012-7094}, coden = {DUMJAO}, mrclass = {11G07 (11S80)}, mrnumber = {93d:11059} } @Book{ artin-tate:cft, author = {Artin, E. and Tate, J.}, title = {Class field theory}, series = {Advanced Book Classics}, edition = {Second}, publisher = {Addison-Wesley Publishing Company Advanced Book Program}, address = {Redwood City, CA}, year = {1990}, pages = {xxxviii+259}, isbn = {0-201-51011-1}, mrclass = {11R37 (11-01 11R34)}, mrnumber = {91b:11129} } @Article{ mahler:inequalities, author = {Mahler, K.}, title = {Inequalities for ideal bases in algebraic number fields}, journal = {J. Austral. Math. Soc.}, volume = {4}, year = {1964}, pages = {425--448}, mrclass = {12.50}, mrnumber = {31 \#1243}, mrreviewer = {L. R. McCulloh} } @Article{ iwasawa:adele, author = {Iwasawa, K.}, title = {On the rings of valuation vectors}, journal = {Ann. of Math. (2)}, volume = {57}, year = {1953}, pages = {331--356}, mrclass = {10.0X}, mrnumber = {14,849a}, mrreviewer = {J. T. Tate} } @Book{ lang:algebraic_numbers, author = {Lang, S.}, title = {Algebraic numbers}, publisher = {Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto-London}, year = {1964}, pages = {ix+163}, mrclass = {10.65}, mrnumber = {28 \#3974}, mrreviewer = {S. Chowla} } @Book{ cassels:lectures, author = {Cassels, J.\thinspace{}W.\thinspace{}S.}, title = {Lectures on elliptic curves}, series = {London Mathematical Society Student Texts}, volume = {24}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {1991}, pages = {vi+137}, isbn = {0-521-41517-9; 0-521-42530-1}, mrclass = {11G05 (14H52)}, mrnumber = {92k:11058}, mrreviewer = {Philippe Satg{\'e}} } @Article{ lenstra:pell, author = {Lenstra, Jr., H.\thinspace{}W.}, title = {Solving the {P}ell equation}, journal = {Notices Amer. Math. Soc.}, fjournal = {Notices of the American Mathematical Society}, volume = {49}, year = {2002}, number = {2}, pages = {182--192}, issn = {0002-9920}, coden = {AMNOAN}, mrclass = {11D09 (01A99 11R27)}, mrnumber = {2002i:11028}, mrreviewer = {Duncan A. Buell} } @Book{ artin:algebra, author = {Artin, M.}, title = {Algebra}, publisher = {Prentice Hall Inc.}, address = {Englewood Cliffs, NJ}, year = {1991}, pages = {xviii+618}, isbn = {0-13-004763-5}, mrclass = {00A05 (11-01 12-01 13-01 15-01 16-01 20-01)}, mrnumber = {92g:00001}, mrreviewer = {Gerald J. Janusz} } @Book{ artin:ant, author = {Artin, E.}, title = {Theory of algebraic numbers}, series = {Notes by Gerhard W\"urges from lectures held at the Mathematisches Institut, G\"ottingen, Germany, in the Winter Semester}, volume = {1956/7}, publisher = {George Striker, Schildweg 12, G\"ottingen}, year = {1959}, pages = {172}, mrclass = {10.65}, mrnumber = {24 \#A1884}, mrreviewer = {L. Carlitz} } @Book{ am, author = {Atiyah, M. F. and Macdonald, I. G.}, title = {Introduction to commutative algebra}, publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.}, year = {1969}, pages = {ix+128}, mrclass = {13.00}, mrnumber = {39 \#4129}, mrreviewer = {J. A. Johnson} } @Article{ agashe, author = {Agashe, A.}, title = {On invisible elements of the {T}ate-{S}hafarevich group}, journal = {C. R. Acad. Sci. Paris S\'er. I Math.}, fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, volume = {328}, year = {1999}, number = {5}, pages = {369--374}, issn = {0764-4442}, coden = {CASMEI}, mrclass = {11Gxx}, mrnumber = {1 678 131} } @article {agashe-stein:bsd, AUTHOR = {Agashe, A. and Stein, W.}, TITLE = {Visible evidence for the {B}irch and {S}winnerton-{D}yer conjecture for modular abelian varieties of analytic rank zero}, NOTE = {With an appendix by J.\ Cremona and B.\ Mazur}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {74}, YEAR = {2005}, NUMBER = {249}, PAGES = {455--484 (electronic)}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {11G40 (11G10)}, MRNUMBER = {2085902}, } @Article{ agashe-ribet-stein:manin, author = "Agashe, A. and Ribet, K.\thinspace{}A. and Stein, W.\thinspace{}A.", title = "The {M}anin {C}onstant", year = {2006}, journal = {JPAM Coates Volume}, note = {\url{http://modular.math.washington.edu/papers/ars-manin/}} } @Article{ agashe-ribet-stein:modular, author = "Agashe, A. and Ribet, K.\thinspace{}A. and Stein, W.\thinspace{}A.", title = "The {M}odular {D}egree, {C}ongruence {P}rimes and {M}ultiplicity {O}ne", year = {2006}, journal = {IMRN Coates Volume}, note = {\url{http://modular.math.washington.edu/papers/ars-congruence/}} } @article {lario-schoof, AUTHOR = {Lario, Joan-C. and Schoof, Ren{\'e}}, TITLE = {Some computations with {H}ecke rings and deformation rings}, NOTE = {With an appendix by Amod Agashe and William Stein}, JOURNAL = {Experiment. Math.}, FJOURNAL = {Experimental Mathematics}, VOLUME = {11}, YEAR = {2002}, NUMBER = {2}, PAGES = {303--311}, ISSN = {1058-6458}, MRCLASS = {11F80 (11F11 11F25)}, MRNUMBER = {MR1959271 (2004b:11072)}, MRREVIEWER = {Lea Terracini}, } @Article{ agashe-stein:visibility, author = {Agashe, A. and Stein, W.}, title = {Visibility of {S}hafarevich-{T}ate groups of abelian varieties}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {97}, year = {2002}, number = {1}, pages = {171--185}, issn = {0022-314X}, coden = {JNUTA9}, mrclass = {11G40 (11G10 14K15)}, mrreviewer = {Chandan Singh Dalawat} } @Article{ agashe:invisible, author = {Agash{\'e}, Amod}, title = {On invisible elements of the {T}ate-{S}hafarevich group}, journal = {C. R. Acad. Sci. Paris S\'er. I Math.}, fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, volume = {328}, year = {1999}, number = {5}, pages = {369--374}, issn = {0764-4442}, coden = {CASMEI}, mrclass = {11G40 (11G10 11G18)}, mrnumber = {2000e:11083}, mrreviewer = {Kenneth Kramer} } @Article{ agashe:phd, author = "Agashe, A.", title = {The {B}irch and {S}winnerton-{D}yer formula for modular abelian varieties of analytic rank~$0$}, journal = {Ph.D. thesis, University of California, Berkeley}, year = {2000} } @Book{ antwerpiv, title = {Modular functions of one variable. {I}{V}}, booktitle = {Proceedings of the International Summer School on Modular Functions of One Variable and Arithmetical Applications, RUCA, University of Antwerp, Antwerp, July 17--August 3, 1972}, editor = {Birch, B.\thinspace{}J. and Kuyk, W.}, note = {Lecture Notes in Mathematics, Vol. 476}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1975}, pages = {iv+151} } @Article{ artin:conjecture, author = {Artin, E.}, title = {{\"U}ber eine neue {A}rt von {L}-Reihen}, journal = {Abh. Math. Sem. Univ. Hamburg}, volume = {3}, year = {1923}, pages = {89--108} } @Article{ artin:conjecture2, author = {Artin, E}, title = {Zur {T}heorie der {L}-{R}eihen mit allgemeinen {G}ruppencharakteren}, journal = {Abh. math. Semin. Univ. Hamburg}, volume = {8}, year = {1930}, pages = {292--306} } @Article{ ash-stevens, author = {Ash, A. and Stevens, G.}, title = {Cohomology of arithmetic groups and congruences between systems of {H}ecke eigenvalues}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {365}, year = {1986}, pages = {192--220}, issn = {0075-4102}, coden = {JRMAA8} } @Article{ atkin-lehner, author = {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.}, title = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}}, journal = {Math. Ann.}, volume = {185}, year = {1970}, pages = {134--160} } @article {bdsbt, AUTHOR = {Buzzard, Kevin and Dickinson, Mark and Shepherd-Barron, Nick and Taylor, Richard}, TITLE = {On icosahedral {A}rtin representations}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {109}, YEAR = {2001}, NUMBER = {2}, PAGES = {283--318}, ISSN = {0012-7094}, CODEN = {DUMJAO}, MRCLASS = {11F80 (11F33 11G18 11R42)}, MRNUMBER = {MR1845181 (2002k:11078)}, MRREVIEWER = {Gebhard B{\"o}ckle}, } @Book{ bgr, author = {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.}, title = {Non-{A}rchimedean analysis: A systematic approach to rigid analytic geometry}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1984}, pages = {xii+436}, isbn = {3-540-12546-9}, mrclass = {32K10 (30G05 46P05)}, mrnumber = {86b:32031}, mrrevr = {W. Bartenwerfer} } @InCollection{ birch:atkin, author = {Birch, B.}, title = {Atkin and the {A}tlas {L}ab}, booktitle = {Proceedings of the conference in honor of A.\thinspace{}O.\thinspace{}L. Atkin held at the University of Illinois, Chicago, IL, September 1995}, pages = {13--20}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1998}, mrclass = {11-03 (01A60 11F30 11F33)}, mrnumber = {99c:11002}, mrrevr = {V. Kumar Murty} } @InCollection{ birch:bsd, author = {Birch, B.\thinspace{}J.}, title = {Elliptic curves over \protect{${\mathbf{Q}}$: {A}} progress report}, booktitle = {1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969)}, pages = {396--400}, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, year = {1971} } @InCollection{ birch:cyclo, author = {Birch, B.\thinspace{}J.}, title = {Cyclotomic fields and {K}ummer extensions}, booktitle = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, pages = {85--93}, publisher = {Thompson, Washington, D.C.}, year = {1967} } @InCollection{ birch:edsac, author = {Birch, B. J.}, title = {Conjectures concerning elliptic curves}, booktitle = {Proceedings of Symposia in Pure Mathematics, VIII}, pages = {106--112}, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, year = {1965}, mrclass = {14.49 (14.40)}, mrnumber = {30 \#4759}, mrreviewer = {J. W. S. Cassels} } @InCollection{ birch:hecke_actions, author = {Birch, B. J.}, title = {Hecke actions on classes of ternary quadratic forms}, booktitle = {Computational number theory (Debrecen, 1989)}, pages = {191--212}, publisher = {de Gruyter}, address = {Berlin}, year = {1991}, mrclass = {11E45 (11E20 11F11 11G05 11Y35)}, mrnumber = {93i:11047}, mrrevr = {Rainer Schulze-Pillot} } @InCollection{ bloch-kato, author = {Bloch, S. and Kato, K.}, title = {\protect{${L}$}-functions and \protect{T}amagawa numbers of motives}, booktitle = {The Grothendieck Festschrift, Vol. \protect{I}}, pages = {333--400}, publisher = {Birkh\"auser Boston}, address = {Boston, MA}, year = {1990} } @Article{ bockle:density, author = {B{\"o}ckle, Gebhard}, title = {On the density of modular points in universal deformation spaces}, journal = {Amer. J. Math.}, fjournal = {American Journal of Mathematics}, volume = {123}, year = {2001}, number = {5}, pages = {985--1007}, issn = {0002-9327}, coden = {AJMAAN}, mrclass = {11F80}, mrnumber = {1 854 117} } @Article{ bolling:sha, author = {B{\"o}lling, Reinhard}, title = {Die {O}rdnung der {S}chafarewitsch-{T}ate-{G}ruppe kann beliebig gro\ss \ werden}, journal = {Math. Nachr.}, volume = {67}, year = {1975}, pages = {157--179}, mrclass = {14K15}, mrnumber = {52 \#5684}, mrreviewer = {J. W. S. Cassels} } @Proceedings{ boston, title = {Modular forms and \protect{F}ermat's last theorem (Boston,MA, 1995)}, editor = {Cornell, G. and Silverman, J.\thinspace{}H. and Stevens, G.}, note = {Papers from the Instructional Conference on Number Theory and Arithmetic Geometry held at Boston University, Boston, MA, August 9--18, 1995}, publisher = {Springer-Verlag}, address = {New York}, year = {1997}, pages = {xx+582}, isbn = {0-387-94609-8} } @Article{ boston-lenstra-ribet, author = {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.} and K.\thinspace{}A. Ribet}, title = {Quotients of group rings arising from two-dimensional representations}, journal = {C. R. Acad. Sci. Paris S\'er. I Math.}, fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, volume = {312}, year = {1991}, number = {4}, pages = {323--328}, issn = {0764-4442}, coden = {CASMEI} } @Article{ breuil-conrad-diamond-taylor, author = {Breuil, C. and Conrad, B. and Diamond, F. and Taylor, R.}, title = {On the modularity of elliptic curves over {$\bold Q$}: wild 3-adic exercises}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {14}, year = {2001}, number = {4}, pages = {843--939 (electronic)}, issn = {0894-0347}, mrclass = {11G05 (11F80 11G07 14G35)}, mrnumber = {2002d:11058}, mrreviewer = {Karl Rubin} } @Article{ brue, author = {Brueggeman, S.}, title = {The non-existence of certain \protect{Galois} extensions unramified outside 5}, journal = {Journal of Number Theory}, volume = {75}, year = {1999}, pages = {47--52} } @Article{ brumer-mcguinness, author = {Brumer, A. and McGuinness, O.}, title = {The behavior of the {M}ordell-{W}eil group of elliptic curves}, journal = {Bull. Amer. Math. Soc. (N.S.)}, fjournal = {American Mathematical Society. Bulletin. New Series}, volume = {23}, year = {1990}, number = {2}, pages = {375--382}, issn = {0273-0979}, coden = {BAMOAD}, note = {Data at \protect{\tt http://oisinmc.com/math/310716/}} } @Article{ brumer:rank, author = {Brumer, A.}, title = {The rank of \protect{${J}\sb 0({N})$}}, note = {Columbia University Number Theory Seminar (New York, 1992)}, journal = {Ast\'erisque}, fjournal = {Ast\'erisque}, number = {228}, year = {1995}, pages = {3, 41--68}, issn = {0303-1179} } @Article{ buhler-gross, author = {Buhler, J.\thinspace{}P. and Gross, B.\thinspace{}H.}, title = {Arithmetic on elliptic curves with complex multiplication. {I}{I}}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {79}, year = {1985}, number = {1}, pages = {11--29}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11G40 (11G05 14K22)}, mrnumber = {86j:11066}, mrreviewer = {Kenneth Kramer} } @Book{ buhler:thesis, author = {Buhler, J.\thinspace{}P.}, title = {Icosahedral \protect{G}alois representations}, note = {Lecture Notes in Mathematics, Vol. 654}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1978}, pages = {ii+143}, isbn = {3-540-08844-X} } @article {bump-friedberg-hoffstein:nonvanishing, AUTHOR = {Bump, Daniel and Friedberg, Solomon and Hoffstein, Jeffrey}, TITLE = {Nonvanishing theorems for {$L$}-functions of modular forms and their derivatives}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {102}, YEAR = {1990}, NUMBER = {3}, PAGES = {543--618}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {11F66 (11F67 11G05 11G40)}, MRNUMBER = {MR1074487 (92a:11058)}, MRREVIEWER = {Alexey A. Panchishkin}, } @Article{ bump-friedberg-hoffstein, author = {Bump, D. and Friedberg, S. and Hoffstein, J.}, title = {Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic \protect{${L}$}-functions and their derivatives}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {131}, year = {1990}, number = {1}, pages = {53--127}, issn = {0003-486X}, coden = {ANMAAH} } @Article{ buzzard-stein:artin, author = {Buzzard, K. and Stein, W.\thinspace{}A.}, title = {A mod five approach to modularity of icosahedral {G}alois representations}, journal = {Pacific J. Math.}, fjournal = {Pacific Journal of Mathematics}, volume = {203}, year = {2002}, number = {2}, pages = {265--282}, issn = {0030-8730}, coden = {PJMAAI}, mrclass = {11F80}, mrnumber = {2003c:11052}, mrreviewer = {Mark Edward Tristan Dickinson} } @Article{ buzzard-taylor, author = {Buzzard, K. and Taylor, R.}, title = {Companion forms and weight one forms}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {149}, year = {1999}, number = {3}, pages = {905--919}, issn = {0003-486X}, coden = {ANMAAH}, mrclass = {11Fxx}, mrnumber = {1 709 306} } @Article{ buzzard:level, author = {Buzzard, K.}, title = {On level-lowering for mod 2 representations}, journal = {preprint} } @Article{ buzzard:t2, author = {Buzzard, Kevin}, title = {On the eigenvalues of the {H}ecke operator {$T\sb 2$}}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {57}, year = {1996}, number = {1}, pages = {130--132}, issn = {0022-314X}, coden = {JNUTA9}, mrclass = {11F25}, mrnumber = {96m:11033}, mrreviewer = {Thomas R. Shemanske} } @Article{ carayol:modell, author = {Carayol, H.}, title = {Sur les \protect{repr\'esentations} galoisiennes modulo \protect{$\ell$ attach\'ees} aux formes modulaires}, journal = {Duke Math. J.}, volume = {59}, year = {1989}, pages = {785--801} } @Article{ carearly, author = "Carayol, H.", title = {Sur les \protect{repr\'esentations} \protect{$\ell$-adiques} \protect{associ\'ees} aux formes modulaires de \protect{Hilbert}}, journal = {Ann. scient. \protect{\'Ec.} Norm. Sup., \protect{$4^{\rm eb}$ s\'erie}}, volume = {19}, year = {1986}, pages = {409--468} } @InProceedings{ casselman, author = {Casselman, W.}, title = {On representations of \protect{${\rm {G}{L}}\sb{2}$} and the arithmetic of modular curves}, booktitle = {Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, pages = {107--141. Lecture Notes in Math., Vol. 349}, publisher = {Springer}, address = {Berlin}, year = {1973} } @Book{ cassels-flynn, author = {Cassels, J.\thinspace{}W.\thinspace{}S. and Flynn, E.\thinspace{}V.}, title = {Prolegomena to a middlebrow arithmetic of curves of genus \protect{$2$}}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {1996}, pages = {xiv+219}, isbn = {0-521-48370-0}, mrclass = {11G30 (11Y50 14G25)}, mrnumber = {97i:11071}, mrrevr = {Joseph H. Silverman} } @Proceedings{ cassels-frohlich, title = {Algebraic number theory}, booktitle = {Proceedings of the instructional conference held at the University of Sussex, Brighton, September 1--17, 1965}, editor = {Cassels, J.\thinspace{}W.\thinspace{}S. and \protect{Fr{\"o}hlich}, A.}, note = {Reprint of the 1967 original}, publisher = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]}, address = {London}, year = {1986}, pages = {xviii+366}, isbn = {0-12-163251-2} } @Article{ cassels:arithmeticiii, author = {Cassels, J.\thinspace{}W.\thinspace{}S.}, title = {{A}rithmetic on curves of genus $1$. {I}{I}{I}. {T}he {T}ate-\v {S}afarevi\v c and {S}elmer groups}, journal = {Proc. London Math. Soc. (3)}, volume = {12}, year = {1962}, pages = {259--296}, mrclass = {14.49}, mrnumber = {29 \#1212} } @Article{ cassels:arithmeticiv, author = {Cassels, J.\thinspace{}W.\thinspace{}S.}, title = {Arithmetic on curves of genus \protect{$1$}. {I}{V}. {P}roof of the {H}auptvermutung}, journal = {J. Reine Angew. Math.}, volume = {211}, year = {1962}, pages = {95--112} } @Article{ cassels:arithmeticv, author = {Cassels, J.\thinspace{}W.\thinspace{}S.}, title = {Arithmetic on curves of genus 1. {V}. {T}wo counterexamples}, journal = {J. London Math. Soc.}, volume = {38}, year = {1963}, pages = {244--248} } @Article{ cassels:bigsha, author = {Cassels, J.\thinspace{}W.\thinspace{}S.}, title = {Arithmetic on curves of genus $1$. {V}{I}. {T}he {T}ate-\v {S}afarevi\v c group can be arbitrarily large}, journal = {J. Reine Angew. Math.}, volume = {214/215}, year = {1964}, pages = {65--70}, mrclass = {14.49 (10.12)}, mrnumber = {29 \#104}, mrreviewer = {P. 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Lectures given at the 3rd session of the {C}entro {I}nternazionale {M}atematico {E}stivo \protect{(CIME)}.}", language = "English", source = "{{L}ecture {N}otes in {M}athematics. 1716. {B}erlin: {S}pringer. viii, 260 p. DM 74.00; oeS 541.00; sFr. 67.50; \sterling 28.50; \$ 52.80 (1999). [ISBN 3-540-66546-3/hbk; ISSN 0075-8434]}", publisher = {Springer-Verlag}, address = {Berlin}, year = {1997}, pages = {260} } @Article{ cmi:problems, author = {Clay Mathematics Institute}, title = {Millennium Prize Problems,\hfill\\{\tt http://www.claymath.org/Millennium\_Prize\_Problems/}} } @Article{ coates-wiles:bsd, author = {Coates, J. and Wiles, A.}, title = {On the conjecture of {B}irch and {S}winnerton-{D}yer}, journal = {Invent. Math.}, volume = {39}, year = {1977}, number = {3}, pages = {223--251}, mrclass = {14G10 (10D15 14G25)}, mrnumber = {57 \#3134}, mrreviewer = {Kenneth A. 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Ann.}, fjournal = {Mathematische Annalen}, volume = {310}, year = {1998}, number = {1}, pages = {119--127}, issn = {0025-5831}, coden = {MAANA}, mrclass = {11F25 (11F11 11F33 11F85)}, mrnumber = {99b:11043}, mrrevr = {Alexey A. Panchishkin} } @Article{ coleman-stein:padicapprox, author = {Coleman, R.}, title = {Approximation of Infinite-Slope Modular Eigenforms By Finite-Slope Eigenforms}, journal = {to appear in the Dwork Proceedings}, year = {2003} } @Article{ coleman-voloch, author = {Coleman, R.\thinspace{}F. and Voloch, J.\thinspace{}F.}, title = {Companion forms and \protect{K}odaira-\protect{S}pencer theory}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {110}, year = {1992}, number = {2}, pages = {263--281}, issn = {0020-9910}, coden = {INVMBH} } @Article{ coleman:banach, author = {Coleman, R.\thinspace{}F.}, title = {$p$-adic {B}anach spaces and families of modular forms}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {127}, year = {1997}, number = {3}, pages = {417--479}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11F33 (11F67 11F85 11G07 14E30)}, mrnumber = {98b:11047}, mrrevr = {Alexey A. Panchishkin} } @Article{ coleman:classical, author = {Coleman, R.\thinspace{}F.}, title = {Classical and overconvergent modular forms}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {124}, year = {1996}, number = {1-3}, pages = {215--241}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11F85 (14G20)}, mrnumber = {97d:11090a}, mrrevr = {Fernando Q. Gouv\^ea} } @Article{ coleman:classical_higher, author = {Coleman, R.\thinspace{}F.}, title = {Classical and overconvergent modular forms of higher level}, journal = {J. Th\'eor. Nombres Bordeaux}, fjournal = {Journal de Th\'eorie des Nombres de Bordeaux}, volume = {9}, year = {1997}, number = {2}, pages = {395--403}, issn = {1246-7405}, mrclass = {11F85 (11F11)}, mrnumber = {99g:11071}, mrrevr = {Conjeeveram S. Rajan} } @Article{ coleman:monodromy, author = {Coleman, R.}, title = {The {M}onodromy {P}airing}, journal = {Asian Math. Journal}, volume = {4}, year = {2000}, pages = {315--330} } @Article{ coleman:serre, author = {Coleman, R.\thinspace{}F.}, title = {Serre's conjecture: {T}he {J}ugentraum of the 20th century}, note = {XII School of Algebra, Part I (Portuguese) (Diamantina, 1992)}, journal = {Mat. Contemp.}, fjournal = {Matem\'atica Contempor\cflex anea}, volume = {6}, year = {1994}, pages = {13--18}, issn = {0103-9059}, mrclass = {12F05 (11F03 12F12)}, mrnumber = {95j:12003}, mrrevr = {Henri Darmon} } @Article{ colmez_fontaine, author = {Colmez, P. and Fontaine, J.-M.}, title = {Construction des repr\'esentations {$p$}-adiques semi-stables}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {140}, year = {2000}, number = {1}, pages = {1--43}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11S23 (14F30 14F40)}, mrnumber = {2001g:11184}, mrreviewer = {Mark Kisin} } @Article{ conrad-diamond-taylor:modularity, author = {Conrad, B. and Diamond, F. and Taylor, R.}, title = {Modularity of certain potentially \protect{B}arsotti-\protect{T}ate \protect{G}alois representations}, journal = {J. Amer. Math. 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Math.}, fjournal = {Experimental Mathematics}, volume = {6}, year = {1997}, number = {2}, pages = {97--107}, issn = {1058-6458} } @Book{ curtis-reiner, author = {Curtis, C.\thinspace{}W. and Reiner, I.}, title = {Representation theory of finite groups and associative algebras}, note = {Pure and Applied Mathematics, Vol. XI}, publisher = {Interscience Publishers, a division of John Wiley \& Sons, New York-London}, year = {1962}, pages = {xiv+685} } @InCollection{ darmon-bsd, author = {Darmon, H.}, title = {Wiles' theorem and the arithmetic of elliptic curves}, booktitle = {Modular forms and Fermat's last theorem (Boston, MA, 1995)}, pages = {549--569}, publisher = {Springer}, address = {New York}, year = {1997}, mrclass = {11G40 (11G05)}, mrnumber = {1 638 495} } @Article{ darmon-merel, author = {Darmon, H. and Merel, L.}, title = {Winding quotients and some variants of {F}ermat's last theorem}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {490}, year = {1997}, pages = {81--100}, issn = {0075-4102}, coden = {JRMAA8}, mrclass = {11G18 (11D41 11F80 11G05)}, mrnumber = {98h:11076}, mrrevr = {Kenneth Kramer} } @InCollection{ darmon:serre, author = {Darmon, Henri}, title = {Serre's conjectures}, booktitle = {Seminar on Fermat's Last Theorem (Toronto, ON, 1993--1994)}, pages = {135--153}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1995}, mrclass = {11F80 (11F11 11R32)}, mrnumber = {96h:11048}, mrrevr = {Dipendra Prasad} } @InCollection{ ddt, author = {Darmon, H. and Diamond, F. and Taylor, R.}, title = {Fermat's last theorem}, booktitle = {Current developments in mathematics, 1995 (Cambridge, MA)}, pages = {1--154}, publisher = {Internat. Press}, address = {Cambridge, MA}, year = {1994} } @InProceedings{ deligne, author = {Deligne, P.}, title = {Formes modulaires et \protect{repr\'{e}sentations $\ell$-adiques.}}, note = {Lecture Notes in Mathematics, Vol. 179}, publisher = {Springer-Verlag}, booktitle = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69}, address = {Berlin and New York}, year = {1971}, pages = {139--172} } @InProceedings{ deligne-rapoport, author = {Deligne, P. and Rapoport, M.}, title = {Les sch\'emas de modules de courbes elliptiques}, booktitle = {Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, pages = {143--316. Lecture Notes in Math., Vol. 349}, publisher = {Springer}, address = {Berlin}, year = {1973} } @Article{ deligne-serre, author = {Deligne, P. and Serre, J-P.}, title = {Formes modulaires de poids $1$}, journal = {Ann. Sci. \'Ecole Norm. Sup. (4)}, volume = {7}, year = {1974}, pages = {507--530 (1975)} } @InCollection{ diamond-im, author = {Diamond, F. and Im, J.}, title = {Modular forms and modular curves}, booktitle = {Seminar on {F}ermat's {L}ast {T}heorem}, pages = {39--133}, pppublisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1995} } @Article{ diamond-kramer, author = {Diamond, F. and Kramer, K.}, title = {Modularity of a family of elliptic curves}, journal = {Math. Res. Lett.}, fjournal = {Mathematical Research Letters}, volume = {2}, year = {1995}, number = {3}, pages = {299--304}, issn = {1073-2780} } @InProceedings{ diamond:refined, author = {Diamond, F.}, title = {The refined conjecture of \protect{S}erre}, booktitle = {Elliptic curves, modular forms, \& \protect{F}ermat's last theorem (\protect{H}ong \protect{K}ong, 1993)}, pages = {22--37}, publisher = {Internat. Press}, address = {Cambridge, MA}, year = {1995} } @Article{ dickinson:thesis, author = {Dickinson, M.}, title = {On the modularity of certain $2$-adic Galois representations}, journal = {Harvard Ph.D. thesis}, year = {2000} } @Book{ dixcohomologie, title = {Dix expos\'es sur la cohomologie des sch\'emas}, note = {Advanced Studies in Pure Mathematics, Vol. 3}, publisher = {North-Holland Publishing Co.}, address = {Amsterdam}, year = {1968}, pages = {vi+386}, mrclass = {14.55}, mrnumber = {39 #2777} } @Article{ doud, author = {Doud, D.}, title = {\protect{${S}\sb 4$} and \protect{$\tilde {S}{}\sb 4$} extensions of \protect{${\bf {Q}}$} ramified at only one prime}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {75}, year = {1999}, number = {2}, pages = {185--197}, issn = {0022-314X}, coden = {JNUTA9} } @Article{ drinfeld:coverings, author = {Drinfeld, V.\thinspace{}G.}, title = {Coverings of \protect{$p$-adic} symmetric domains}, journal = {Funkcional. Anal. i Prilov zen.}, volume = {10}, year = {1976}, number = {2}, pages = {29--40} } @Article{ dummigan-stein-watkins:motives, author = {Dummigan, N. and Watkins, M. and Stein, W.\thinspace{}A.}, title = {{Constructing Elements in Shafarevich-Tate Groups of Modular Motives}}, journal = {Number theory and algebraic geometry, ed. by Miles Reid and Alexei Skorobogatov}, year = {2003}, volume = {303}, series = {Lecture Notes Series}, publisher = {Cambridge Univ. Press}, pages = {91--118} } @Article{ dummigan:cp, AUTHOR = {Dummigan, N.}, TITLE = {Period ratios of modular forms}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {318}, YEAR = {2000}, NUMBER = {3}, PAGES = {621--636}, ISSN = {0025-5831}, CODEN = {MAANA}, MRCLASS = {11F67 (11F33 11G40)}, MRNUMBER = {MR1800772 (2002a:11049)}, MRREVIEWER = {Kevin L. James}, } @article {dummigan:congruences, AUTHOR = {Dummigan, N.}, TITLE = {Congruences of modular forms and {S}elmer groups}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {8}, YEAR = {2001}, NUMBER = {4}, PAGES = {479--494}, ISSN = {1073-2780}, MRCLASS = {11F33 (11F37 11F67 11G40)}, MRNUMBER = {MR1849264 (2002k:11064)}, MRREVIEWER = {Andrea Mori}, } @Article{ edixcole, author = {Coleman, R.\thinspace{}F. and Edixhoven, B.}, title = {On the semi-simplicity of the \protect{${U}\sb p$}-operator on modular forms}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {310}, year = {1998}, number = {1}, pages = {119--127}, issn = {0025-5831}, coden = {MAANA} } @Article{ edixhoven:comparison, author = {Edixhoven, B.}, title = {Comparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod~$2$ of weight one}, year = {July, 2003}, journal = {preprint} } @Article{ edixhoven:eisen, author = {Edixhoven, B.}, title = {L'action de l'alg\`ebre de \protect{H}ecke sur les groupes de composantes des jacobiennes des courbes modulaires est ``\protect{E}isenstein''}, note = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)}, journal = {Ast\'erisque}, fjournal = {Ast\'erisque}, number = {196--197}, year = {1991}, pages = {7--8, 159--170 (1992)}, issn = {0303-1179} } @Article{ edixhoven:erratum, author = {Edixhoven, B.}, title = {Erratum and addendum: ``{T}he role of {S}erre's conjecture in the proof of {F}ermat's theorem''}, journal = {Gaz. Math.}, fjournal = {Gazette des Math\'ematiciens}, number = {67}, year = {1996}, pages = {19}, issn = {0224-8999}, mrclass = {11F33 (11D41 11F80 11G05)}, mrnumber = {96k:11055b}, mrrevr = {Fernando Q. Gouv\^ea} } @InCollection{ edixhoven:manin, author = {Edixhoven, B.}, title = {On the {M}anin constants of modular elliptic curves}, booktitle = {Arithmetic algebraic geometry (Texel, 1989)}, pages = {25--39}, publisher = {Birkh\"auser Boston}, address = {Boston, MA}, year = {1991}, mrclass = {11G05 (14G25)}, mrnumber = {92a:11066}, mrreviewer = {Philippe Satg{\'e}} } @Article{ edixhoven:minimal, author = {Edixhoven, B.}, title = {Minimal resolution and stable reduction of \protect{${X}\sb 0({N})$}}, journal = {Ann. Inst. Fourier (Grenoble)}, fjournal = {Universit\'e de Grenoble. Annales de l'Institut Fourier}, volume = {40}, year = {1990}, number = {1}, pages = {31--67}, issn = {0373-0956}, coden = {AIFUA7}, mrclass = {11G18 (14G35)}, mrnumber = {92f:11080}, mrreviewer = {Autorreferat} } @InProceedings{ edixhoven:serre, author = {Edixhoven, B.}, title = {Serre's conjecture}, booktitle = {Modular forms and \protect{F}ermat's last theorem (Boston, MA, 1995)}, pages = {209--242}, publisher = {Springer}, address = {New York}, year = {1997} } @Article{ edixhoven:serrerole, author = {Edixhoven, B.}, title = {Le r\^{o}le de la conjecture de {S}erre dans la d\'emonstration du th\'eor\`eme de {F}ermat}, journal = {Gaz. Math.}, fjournal = {Gazette des Math\'ematiciens}, number = {66}, year = {1995}, pages = {25--41}, issn = {0224-8999}, mrclass = {11F33 (11D41 11F80 11G05)}, mrnumber = {96k:11055a}, mrrevr = {Fernando Q. Gouv\^ea} } @Article{ edixhoven:tame, author = {Edixhoven, B.}, title = {N\'eron models and tame ramification}, journal = {Compositio Math.}, fjournal = {Compositio Mathematica}, volume = {81}, year = {1992}, number = {3}, pages = {291--306}, issn = {0010-437X}, coden = {CMPMAF}, mrclass = {14K15 (11G10)}, mrnumber = {93a:14041}, mrreviewer = {Min Ho Lee} } @Article{ edixhoven:weight, author = {Edixhoven, B.}, title = {The weight in \protect{S}erre's conjectures on modular forms}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {109}, year = {1992}, number = {3}, pages = {563--594}, issn = {0020-9910}, coden = {INVMBH} } @Article{ ega4_1, author = {Grothendieck, A.}, title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {I}}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, number = {20}, year = {1964}, pages = {259}, mrclass = {14.05 (13.10)}, mrnumber = {30 \#3885}, mrreviewer = {H. Hironaka} } @Article{ ega4_2, author = {Grothendieck, A.}, title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {I}{I}}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, number = {24}, year = {1965}, pages = {231}, mrclass = {14.00}, mrnumber = {33 \#7330}, mrreviewer = {H. Hironaka} } @Article{ ega4_3, author = {Grothendieck, A.}, title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {I}{I}{I}}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, number = {28}, year = {1966}, pages = {255}, mrclass = {14.55}, mrnumber = {36 \#178}, mrreviewer = {J. P. Murre} } @Article{ ega4_4, author = {Grothendieck, A.}, title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas {I}{V}}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, number = {32}, year = {1967}, pages = {361}, mrclass = {14.55}, mrnumber = {39 \#220}, mrreviewer = {J. P. Murre} } @Article{ eichler:ideal, author = {Eichler, M.}, title = {Uber die Idealklassenzahl total definiter Quaternionenalgebren}, journal = {Math. Zeit.}, volume = {43}, year = {1937}, pages = {102--109} } @Article{ eichler:quadratic, author = {Eichler, M.}, title = {Quadratische \protect{F}ormen und \protect{M}odulfunktionen}, journal = {Acta Arith.}, volume = {4}, year = {1958}, pages = {217--239} } @InCollection{ eigencurve, author = {Coleman, R. and Mazur, B.}, title = {The {E}igencurve}, booktitle = {Galois representations in arithmetic algebraic geometry (Durham, 1996)}, pages = {1--113}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, year = {1998}, mrclass = {11Fxx (11Gxx)}, mrnumber = {1 696 469} } @Book{ eisenbud, author = {Eisenbud, D.}, title = {Commutative Algebra with a View Toward Algebraic Geometry}, publisher = {Springer-Verlag}, address = {New York}, year = {1995}, pages = {xvi+785}, isbn = {0-387-94268-8; 0-387-94269-6}, mrclass = {13-01 (14A05)}, mrnumber = {97a:13001}, mrrevr = {Matthew Miller} } @Book{ eisenbud-harris, author = {Eisenbud, D. and Harris, J.}, title = {{S}chemes, {T}he language of modern algebraic geometry}, publisher = {Wadsworth \& Brooks/Cole Advanced Books \& Software}, address = {Pacific Grove, CA}, year = {1992}, pages = {xii+157}, isbn = {0-534-17606-2; 0-534-17604-6}, mrclass = {14-01 (14A15)}, mrnumber = {93k:14001}, mrrevr = {Alexey N. Rudakov} } @Book{ eisenbud-harris-2, author = {Eisenbud, D. and Harris, J.}, title = {{S}chemes, {T}he language of modern algebraic geometry}, note = {Graduate Texts in Mathematics, Vol.\ 197}, publisher = {Springer-Verlag}, address = {Berlin}, year = {}, pages = {} } @Book{ eisenbud_harris:geometry, author = {Eisenbud, D. and Harris, J.}, title = {The geometry of schemes}, publisher = {Springer-Verlag}, address = {New York}, year = {2000}, pages = {x+294}, isbn = {0-387-98638-3; 0-387-98637-5}, mrclass = {14A15 (14-01 14C05 14H50 14N05)}, mrnumber = {2001d:14002}, mrreviewer = {Allen B. Altman} } @InCollection{ elkies:ffield, author = {Elkies, N.\thinspace{}D.}, title = {Elliptic and modular curves over finite fields and related computational issues}, booktitle = {Computational perspectives on number theory (Chicago, IL, 1995)}, pages = {21--76}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1998} } @InCollection{ elkies:heegner, author = {Elkies, N.\thinspace{}D.}, title = {Heegner point computations}, booktitle = {Algorithmic number theory (Ithaca, NY, 1994)}, pages = {122--133}, publisher = {Springer}, address = {Berlin}, year = {1994} } @Article{ ellenberg-skinner:modularity, author = {Ellenberg, J. and Skinner, C.}, title = {On the {M}odularity of {$\Q$}-curves}, journal = {{\tt http://www.math.princeton.edu/~ellenber/papers.html\#QCURVE}} , year = {2000} } @Article{ ellenberg:qcurves_survey, author = {Ellenberg, J.}, title = {$\Q$-curves and {G}alois {R}epresentations}, journal = {{\tt http://www.math.princeton.edu/~ellenber/papers.html\#MCAV}}, year = {2002} } @Article{ emerton:optimal, author = {Emerton, M.}, title = {Optimal {Q}uotients of {M}odular {J}acobians}, journal = {preprint}, year = {2001} } @Article{ empirical, author = {Flynn, E.\thinspace{}V. and \protect{Lepr\'{e}vost}, F. and Schaefer, E.\thinspace{}F. and Stein, W.\thinspace{}A. and Stoll, M. and Wetherell, J.\thinspace{}L.}, title = {Empirical evidence for the {B}irch and {S}winnerton-{D}yer conjectures for modular {J}acobians of genus 2 curves}, journal = {Math. Comp.}, fjournal = {Mathematics of Computation}, volume = {70}, year = {2001}, number = {236}, pages = {1675--1697 (electronic)}, issn = {0025-5718}, coden = {MCMPAF}, mrclass = {}, mrnumber = {1 836 926} } @Article{ faltings-finiteness, author = {Faltings, G.}, title = {\protect{Endlichkeitss\"atze f\"ur} abelsche \protect{V}ariet\"aten \"uber \protect{Z}ahlk\"orpern}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {73}, year = {1983}, number = {3}, pages = {349--366}, issn = {0020-9910}, coden = {INVMBH} } @Article{ faltings-jordan, author = {Faltings, G. and Jordan, B.\thinspace{}W.}, title = {Crystalline cohomology and \protect{${\rm {G}{L}}(2,{\bf {Q}})$}}, journal = {Israel J. Math.}, fjournal = {Israel Journal of Mathematics}, volume = {90}, year = {1995}, number = {1-3}, pages = {1--66}, issn = {0021-2172}, coden = {ISJMAP} } @InCollection{ faltings:finiteness, author = {Faltings, G.}, title = {Finiteness theorems for abelian varieties over number fields}, booktitle = {Arithmetic geometry (Storrs, Conn., 1984)}, pages = {9--27}, note = {Translated from the German original [Invent.\ Math.\ {\bf 73} (1983), no.\ 3, 349--366; ibid.\ {\bf 75} (1984), no.\ 2, 381; MR 85g:11026ab] by Edward Shipz}, publisher = {Springer}, address = {New York}, year = {1986}, mrclass = {11G10 (14K15)}, mrnumber = {861 971} } @Article{ farmer-james:maeda, author = {Farmer, D. W. and James, K.}, title = {The irreducibility of some level 1 {H}ecke polynomials}, journal = {Math. Comp.}, fjournal = {Mathematics of Computation}, volume = {71}, year = {2002}, number = {239}, pages = {1263--1270 (electronic)}, issn = {0025-5718}, coden = {MCMPAF}, mrclass = {11F25 (11F11)}, mrnumber = {2003e:11046}, mrreviewer = {T. C. Vasudevan} } @Article{ fearnley:phd, author = {Fearnley, J.}, title = {{V}anishing and {N}on-{V}anishing of {L}-Series of {E}lliptic {C}urves {T}wisted by {D}irichlet {C}haracters}, year = 2001, journal = {Concordia Ph.D. thesis} } @Article{ flach:pairing, author = {Flach, M.}, title = {A generalisation of the {C}assels-{T}ate pairing}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {412}, year = {1990}, pages = {113--127}, issn = {0075-4102}, coden = {JRMAA8}, mrclass = {11G09 (11R23 11S25)}, mrnumber = {92b:11037}, mrreviewer = {Vincent Fleckinger} } @Article{ fontaine:groupes, author = {Fontaine, J-M.}, title = {Groupes finis commutatifs sur les vecteurs de {W}itt}, journal = {C. R. Acad. Sci. Paris S\'er. A-B}, volume = {280}, year = {1975}, pages = {Ai, A1423--A1425}, mrclass = {14L05}, mrnumber = {51 \#10353}, mrreviewer = {Robert A. Morris} } @InCollection{ frey-muller, author = {Frey, G. and M{\"u}ller, M.}, title = {Arithmetic of modular curves and applications}, booktitle = {Algorithmic algebra and number theory (Heidelberg, 1997)}, pages = {11--48}, publisher = {Springer}, address = {Berlin}, year = {1999} } @InProceedings{ frey:boston, author = {Frey, G.}, title = {On ternary equations of \protect{F}ermat type and relations with elliptic curves}, booktitle = {Modular forms and \protect{F}ermat's last theorem (Boston, MA, 1995)}, pages = {527--548}, publisher = {Springer}, address = {New York}, year = {1997}, crossref = "boston" } @Book{ freyetal, title = {On {A}rtin's conjecture for odd 2-dimensional representations}, booktitle = {On {A}rtin's conjecture for odd 2-dimensional representations}, editor = {Frey, G.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1994}, pages = {viii+148}, isbn = {3-540-58387-4} } @Article{ freyone, author = {Frey, G.}, title = {Links between stable elliptic curves and certain {D}iophantine \protect{\nobreak{equations}}}, journal = {Ann. Univ. Sarav. Ser. Math.}, fjournal = {Annales Universitatis Saraviensis. Series Mathematicae}, volume = {1}, year = {1986}, number = {1}, pages = {iv+40} } @InCollection{ freytwo, author = {Frey, G.}, title = {Links between solutions of \protect{${A}-{B}={C}$} and elliptic curves}, booktitle = {Number theory (Ulm, 1987)}, pages = {31--62}, publisher = {Springer}, address = {New York}, year = {1989} } @InCollection{ frohlich:local, author = {Fr{\"o}hlich, A.}, title = {Local fields}, booktitle = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965) }, pages = {1--41}, publisher = {Thompson, Washington, D.C.}, year = {1967} } @Article{ fujiwara, author = {Fujiwara, K.}, title = {Level optimization in the totally real case}, journal = {in preparation}, year = {1999} } @Article{ galbraith, author = {Galbraith, S.\thinspace{}D.}, title = {Equations for modular curves}, year = {1996}, journal = {Oxford Ph.D. thesis}, pages = {91 pp.} } @article {gonz-lario:manin, AUTHOR = {Gonz{\'a}lez, Josep and Lario, Joan-C.}, TITLE = {{$\bold Q$}-curves and their {M}anin ideals}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {123}, YEAR = {2001}, NUMBER = {3}, PAGES = {475--503}, ISSN = {0002-9327}, CODEN = {AJMAAN}, MRCLASS = {11G05 (11G18)}, MRNUMBER = {MR1833149 (2002e:11070)}, MRREVIEWER = {Ivica Gusi{\'c}}, } @Article{ generatinghecke, author = "Agashe, A. and Stein, W.\thinspace{}A.", title = {Generating the \protect{H}ecke algebra}, journal = {preprint}, year = {1999} } @Article{ goldfeld:complexity, author = {Goldfeld, D.}, title = {On the computational complexity of modular symbols}, journal = {Math. Comp.}, fjournal = {Mathematics of Computation}, volume = {58}, year = {1992}, number = {198}, pages = {807--814}, issn = {0025-5718}, coden = {MCMPAF}, mrclass = {11F67 (11Y35)}, mrnumber = {93a:11042}, mrrevr = {Glenn Stevens} } @Article{ goldfeld:l1, author = {Goldfeld, D.}, title = {Sur les produits partiels eul\'eriens attach\'es aux courbes elliptiques}, journal = {C. R. Acad. Sci. Paris S\'er. I Math.}, fjournal = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, volume = {294}, year = {1982}, number = {14}, pages = {471--474}, issn = {0249-6321}, coden = {CHASAP}, mrclass = {14K15 (12A70 14G10 14K07)}, mrnumber = {84d:14031}, mrreviewer = {Andrew Bremner} } @Article{ gonzalez-lario:manin, author = {Gonz{\'a}lez, J. and Lario, J.-C.}, title = {{$\mathbf{Q}$}-curves and their {M}anin ideals}, journal = {Amer. J. Math.}, fjournal = {American Journal of Mathematics}, volume = {123}, year = {2001}, number = {3}, pages = {475--503}, issn = {0002-9327}, coden = {AJMAAN}, mrclass = {11G05 (11G18)}, mrnumber = {2002e:11070}, mrreviewer = {Ivica Gusi{\'c}} } @Article{ mcgraw-ono:vis, AUTHOR = {McGraw, William J. and Ono, Ken}, TITLE = {Modular form congruences and {S}elmer groups}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {67}, YEAR = {2003}, NUMBER = {2}, PAGES = {302--318}, ISSN = {0024-6107}, CODEN = {JLMSAK}, MRCLASS = {11F33 (11F37 11F67 11G40)}, MRNUMBER = {MR1956137 (2004d:11033)}, MRREVIEWER = {Vinayak Vatsal}, } @InCollection{ gouvea-mazur:density, author = {Gouv\^{e}a, F.\thinspace{}Q. and Mazur, B.}, title = {On the density of modular representations}, booktitle = {Computational perspectives on number theory (Chicago, IL, 1995)}, pages = {127--142}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1998}, mrclass = {11F33 (11F80)}, mrnumber = {99a:11056}, mrreviewer = {Andrea Mori} } @Article{ gouvea-mazur:families, author = {Gouv\^ea, F. and Mazur, B.}, title = {Families of modular eigenforms}, journal = {Math. Comp.}, fjournal = {Mathematics of Computation}, volume = {58}, year = {1992}, number = {198}, pages = {793--805}, issn = {0025-5718}, coden = {MCMPAF}, mrclass = {11F33 (11Y35 14G20)}, mrnumber = {93d:11049}, mrrevr = {Bas Edixhoven} } @Article{ gouvea:ordinary, author = {Gouv\^ea, F.\thinspace{}Q.}, title = {On the ordinary {H}ecke algebra}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {41}, year = {1992}, number = {2}, pages = {178--198}, issn = {0022-314X}, coden = {JNUTA9} } @Book{ gouvea:slnm, author = {Gouv\^{e}a, F.\thinspace{}Q.}, title = {Arithmetic of $p$-adic modular forms}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1988}, pages = {viii+121}, isbn = {3-540-18946-7}, mrclass = {11F85 (11F80)}, mrnumber = {91e:11056}, mrreviewer = {Alexey A. Panchishkin} } @Book{ greenberg-harper, author = {Greenberg, M.\thinspace{}J. and Harper, J.\thinspace{}R.}, title = {Algebraic topology}, note = {A first course}, publisher = {Benjamin/Cummings Publishing Co. Inc. Advanced Book Program}, address = {Reading, Mass.}, year = {1981}, pages = {xi+311 pp. (loose errata)}, isbn = {0-8053-3558-7; 0-8053-3557-9}, mrclass = {55-01}, mrnumber = {83b:55001}, mrrevr = {J. P. May} } @Article{ gross-kohnen-zagier, author = {Gross, B. and Kohnen, W. and Zagier, D.}, title = {Heegner points and derivatives of ${L}$-series. {I}{I}}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {278}, year = {1987}, number = {1-4}, pages = {497--562}, issn = {0025-5831}, coden = {MAANA3}, mrclass = {11G40 (11F30 11G05 11R29 14G10)}, mrnumber = {89i:11069}, mrrevr = {Lawrence Washington} } @Article{ gross-zagier, author = {Gross, B. and Zagier, D.}, title = {Heegner points and derivatives of \protect{${L}$}-series}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {84}, year = {1986}, number = {2}, pages = {225--320}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11G40 (11F11 11G05 14G10)}, mrnumber = {87j:11057}, mrrevr = {Loren D. Olson} } @InCollection{ gross:central, author = {Gross, B.\thinspace{}H.}, title = {${L}$-functions at the central critical point}, booktitle = {Motives (Seattle, WA, 1991)}, pages = {527--535}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1994}, mrclass = {11G40 (14G10)}, mrnumber = {95a:11060}, mrrevr = {Jan Nekov{\'a}{\v{r}}} } @InCollection{ gross:kolyvagin, author = {Gross, B.\thinspace{}H.}, title = {Kolyvagin's work on modular elliptic curves}, booktitle = {$L$-functions and arithmetic (Durham, 1989)}, pages = {235--256}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, year = {1991} } @Article{ gross:tameness, author = {Gross, B.\thinspace{}H.}, title = {A tameness criterion for \protect{G}alois representations associated to modular forms (mod \protect{$p$})}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {61}, year = {1990}, number = {2}, pages = {445--517}, issn = {0012-7094}, coden = {DUMJAO} } @Article{ gross_kudla, author = {Gross, B.\thinspace{}H. and Kudla, S.\thinspace{}S.}, title = {Heights and the central critical values of triple product {$L$}-functions}, journal = {Compositio Math.}, fjournal = {Compositio Mathematica}, volume = {81}, year = {1992}, number = {2}, pages = {143--209}, issn = {0010-437X}, coden = {CMPMAF}, mrclass = {11F66 (11F67 11G40 19F27)}, mrnumber = {93g:11047}, mrreviewer = {Alexey A. Panchishkin} } @InCollection{ grothendieck:brauer1, author = {Grothendieck, Alexander}, title = {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et interpr\'etations diverses}, booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas}, pages = {46--66}, publisher = {North-Holland}, address = {Amsterdam}, year = {1968}, mrclass = {14.55}, mrnumber = {39 #5586a} } @InCollection{ grothendieck:brauer2, author = {Grothendieck, Alexander}, title = {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique}, booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas}, pages = {67--87}, publisher = {North-Holland}, address = {Amsterdam}, year = {1968}, mrclass = {14.55}, mrnumber = {39 #5586b} } @InCollection{ grothendieck:brauer3, author = {Grothendieck, Alexander}, title = {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et compl\'ements}, booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas}, pages = {88--188}, publisher = {North-Holland}, address = {Amsterdam}, year = {1968}, mrclass = {14.55}, mrnumber = {39 #5586c}, mrrevr = {J. S. Milne} } @Book{ grothendieck:monodromie, author = {Grothendieck, A.}, title = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. \protect{I}}, note = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie 1967--1969 (SGA 7 I), Dirig\'e par A. Grothendieck. Avec la collaboration de M. Raynaud et D. S. Rim, Lecture Notes in Mathematics, Vol. 288}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1972}, pages = {viii+523} } @InCollection{ gruenberg, author = {Gruenberg, K.}, title = {Profinite groups}, booktitle = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, pages = {116--127}, publisher = {Thompson, Washington, D.C.}, year = {1967} } @Article{ guerzhoy:kummer, title = {Searching for {K}ummer congruences in an infinite slope family}, author = {Guerzhoy, P.}, year = {2000}, journal = {Preprint} } @Book{ guy:unsolved, author = {Guy, R.\thinspace{}K.}, title = {Unsolved problems in number theory}, edition = {Second}, note = {Unsolved Problems in Intuitive Mathematics, I}, publisher = {Springer-Verlag}, address = {New York}, year = {1994}, pages = {xvi+285}, isbn = {0-387-94289-0}, mrclass = {11-01 (00A07 11-02)}, mrnumber = {96e:11002}, mrreviewer = {B. M. M. de Weger} } @Book{ haberland, author = {Haberland, Klaus}, title = {Galois cohomology of algebraic number fields}, note = {With two appendices by Helmut Koch and Thomas Zink}, publisher = {VEB Deutscher Verlag der Wissenschaften}, address = {Berlin}, year = {1978}, pages = {145}, mrclass = {12A60}, mrnumber = {81i:12009}, mrrevr = {Chih-Han Sah} } @Book{ halmos:naive, author = {Halmos, Paul R.}, title = {Naive set theory}, series = {The University Series in Undergraduate Mathematics}, publisher = {D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New York}, year = {1960}, pages = {vii+104}, mrclass = {04.00}, mrnumber = {22 \#5575}, mrreviewer = {L. Rieger} } @Article{ hardy_littlewood:conjf, author = {Hardy, G.\thinspace{}H. and Littlewood, J.\thinspace{}E.}, title = {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}. {O}n the {E}xpression of a {N}umber as a {S}um of {P}rimes.}, journal = {Acta. Math.}, volume = {44}, year = {1922}, pages = {1--70} } @Book{ hartshorne, author = {Hartshorne, R.}, title = {Algebraic {G}eometry}, note = {Graduate Texts in Mathematics, No. 52}, publisher = {Springer-Verlag}, address = {New York}, year = {1977}, pages = {xvi+496}, isbn = {0-387-90244-9} } @Article{ hatada:eigenvalues79, author = {Hatada, K.}, title = {Eigenvalues of {H}ecke operators on \protect{${\rm {S}{L}}(2,\,{\bf {Z}})$}}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {239}, year = {1979}, number = {1}, pages = {75--96}, issn = {0025-5831}, coden = {MAANA3}, mrclass = {10D15}, mrnumber = {80b:10037}, mrreviewer = {Roy Fuller} } @Article{ hatada:general, author = {Hatada, K.}, title = {On classical and {$l$}-adic modular forms of levels {$Nl\sp m$} and {$N$}}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {87}, year = {2001}, number = {1}, pages = {1--14}, issn = {0022-314X}, coden = {JNUTA9}, mrclass = {11F11 (11F80 11F85)}, mrnumber = {2002e:11054}, mrreviewer = {Luis V. Dieulefait} } @Article{ hatada:rationality, author = {Hatada, K.}, title = {Multiplicity one theorem and modular symbols}, journal = {J. Math. Soc. Japan}, fjournal = {Journal of the Mathematical Society of Japan}, volume = {33}, year = {1981}, number = {3}, pages = {445--470}, issn = {0025-5645}, coden = {NISUBC}, mrclass = {10D12 (12A65)}, mrnumber = {83d:10030}, mrrevr = {Wen Ch'ing Winnie Li} } @Book{ hellegouarch:invitation, author = {Hellegouarch, Y.}, title = {Invitation aux math\'ematiques de {F}ermat-{W}iles}, publisher = {Masson}, address = {Paris}, year = {1997}, pages = {viii+401}, isbn = {2-225-83008-8}, mrclass = {11-01 (11D41 11F11 11G05 11G18)}, mrnumber = {99e:11001}, mrrevr = {Massimo Bertolini} } @Article{ hida:invent86, author = {Hida, H.}, title = {Galois representations into \protect{${\rm {G}{L}}\sb 2({\bf {Z}}\sb p[[{X}]])$} attached to ordinary cusp forms}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {85}, year = {1986}, number = {3}, pages = {545--613}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11F11 (11F33 11F85 11R23)}, mrnumber = {87k:11049}, mrrevr = {Ernst-Wilhelm Zink} } @Article{ hida:iwasawa, author = {Hida, H.}, title = {Iwasawa modules attached to congruences of cusp forms}, journal = {Ann. Sci. \'Ecole Norm. Sup. (4)}, fjournal = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme S\'erie}, volume = {19}, year = {1986}, number = {2}, pages = {231--273}, issn = {0012-9593}, coden = {ASENAH}, mrclass = {11F33 (11G18 11R23)}, mrnumber = {88i:11023}, mrrevr = {Yasutaka Ihara} } @Article{ hida:modularity, author = {Hida, H.}, title = {Modularity {P}roblems of {$\Q$}-{M}otives and {B}ase-{C}hange}, journal = {Preprint, {\tt http://www.math.ucla.edu/~hida/}}, year = {2000} } @Article{ hijikata:trace, author = {Hijikata, H.}, title = {Explicit formula of the traces of \protect{H}ecke operators for \protect{$\Gamma_0(N)$}}, journal = {J. Math. Soc. Japan}, number = {1}, volume = {26}, year = {1974}, pages = {56--82} } @Book{ hindry-silverman:diophantine, author = {Hindry, Marc and Silverman, Joseph H.}, title = {Diophantine geometry}, note = {An introduction}, publisher = {Springer-Verlag}, address = {New York}, year = {2000}, pages = {xiv+558}, isbn = {0-387-98975-7; 0-387-98981-1}, mrclass = {11Gxx (11-02 11G10 11G30 11G50 14G25)}, mrnumber = {2001e:11058}, mrreviewer = {Dino J. Lorenzini} } @InProceedings{ hpf, author = {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.}, title = {On $\ell$-adic representations and congruences for coefficients of modular forms}, booktitle = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, pages = {1--55. Lecture Notes in Math., Vol. 350}, publisher = {Springer}, address = {Berlin}, year = {1973} } @Article{ igusa:fibre, author = {Igusa, J.}, title = {Fibre systems of \protect{J}acobian varieties}, journal = {Amer. J. Math.}, volume = {78}, year = {1956}, pages = {171--199} } @Book{ jacquet-langlands, author = {Jacquet, H. and Langlands, R.\thinspace{}P.}, title = {Automorphic forms on \protect{${\rm {G}{L}}(2)$}}, note = {Lecture Notes in Mathematics, Vol. 114}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1970}, pages = {vii+548} } @Article{ jarvis:hilbert, author = {Jarvis, F.}, title = {On \protect{G}alois representations associated to \protect{H}ilbert modular forms}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {491}, year = {1997}, pages = {199--216}, issn = {0075-4102}, coden = {JRMAA8} } @Article{ jarvis:level, author = {Jarvis, F.}, title = {Level lowering for modular mod \protect{$\ell$} representations over totally real fields\-}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {313}, year = {1999}, number = {1}, pages = {141--160}, issn = {0025-5831}, coden = {MAANA} } @Article{ jarvis:mazur, author = {Jarvis, F.}, title = {Mazur's principle for totally real fields of odd degree}, journal = {Compositio Math.}, fjournal = {Compositio Mathematica}, volume = {116}, year = {1999}, number = {1}, pages = {39--79}, issn = {0010-437X}, coden = {CMPMAF} } @InCollection{ jochnowitz:conjecture, author = {Jochnowitz, N.}, title = {A $p$-adic conjecture about derivatives of ${L}$-series attached to modular forms}, booktitle = {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer conjecture}, pages = {239--263}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1994}, mrclass = {11F33 (11F67 11F85 11G40)}, mrnumber = {95g:11037}, mrrevr = {Andrea Mori} } @Article{ jochnowitz:duke, author = {Jochnowitz, N.}, title = {The index of the {H}ecke ring, ${T}\sb{k}$, in the ring of integers of \protect{${T}\sb{k}\otimes {\bf {Q}}$}}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {46}, year = {1979}, number = {4}, pages = {861--869}, issn = {0012-7094}, coden = {DUMJAO}, mrclass = {10D12}, mrnumber = {80k:10023}, mrrevr = {Henri Cohen} } @Article{ jochnowitz:local, author = {Jochnowitz, N.}, title = {A study of the local components of the \protect{H}ecke algebra mod \protect{$\ell$}}, journal = {Trans. Amer. Math. 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Soc.}, fjournal = {The Bulletin of the London Mathematical Society}, volume = {31}, year = {1999}, number = {6}, pages = {681--685}, issn = {0024-6093}, coden = {LMSBBT}, mrclass = {11G18 (11G10 14G35)}, mrnumber = {2000j:11090}, mrreviewer = {Chandrashekhar Khare} } @Article{ joshi, author = {Joshi, K.}, title = {Remarks on methods of {F}ontaine and {F}altings}, journal = {Internat. Math. Res. Notices}, fjournal = {International Mathematics Research Notices}, volume = {1999}, number = {22}, pages = {1199--1209}, issn = {1073-7928}, mrclass = {11Fxx}, mrnumber = {1 731 472} } @InProceedings{ jps, author = {Serre, J-P.}, title = {Congruences et formes modulaires [d'apr\`es {H}.\thinspace{}{P}.\thinspace{}{F}.\ {S}winnerton-{D}yer]}, booktitle = {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No. 416}, pages = {319--338. Lecture Notes in Math., Vol. 317}, publisher = {Springer}, address = {Berlin}, year = {1973} } @article {kato:secret, AUTHOR = {Kato, Kazuya}, TITLE = {{$p$}-adic {H}odge theory and values of zeta functions of modular forms}, NOTE = {Cohomologies $p$-adiques et applications arithm\'etiques. III}, JOURNAL = {Ast\'erisque}, FJOURNAL = {Ast\'erisque}, NUMBER = {295}, YEAR = {2004}, PAGES = {ix, 117--290}, ISSN = {0303-1179}, MRCLASS = {11F85 (11F67 11G40 11R33 11S80 14G10 14G35)}, MRNUMBER = {MR2104361}, } @Article{ katz:annals75, author = {Katz, N.\thinspace{}M.}, title = {Higher congruences between modular forms}, journal = {Ann. of Math. (2)}, volume = {101}, year = {1975}, pages = {332--367}, mrclass = {10D05 (14K15)}, mrnumber = {54 #5120}, mrrevr = {Neal Koblitz} } @InProceedings{ katz:antwerp350, author = {Katz, N.\thinspace{}M.}, title = {$p$-adic properties of modular schemes and modular forms}, booktitle = {Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, pages = {69--190. Lecture Notes in Mathematics, Vol. 350}, publisher = {Springer}, address = {Berlin}, year = {1973} } @Article{ katz:torsion, author = {Katz, N.\thinspace{}M.}, title = {Galois properties of torsion points on abelian varieties}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {62}, year = {1981}, number = {3}, pages = {481--502}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {14K15 (10D35 14G05)}, mrnumber = {82d:14025}, mrreviewer = {Kenneth A. Ribet} } @InProceedings{ katzbonn, author = {Katz, N.\thinspace{}M.}, title = {A result on modular forms in characteristic $p$}, booktitle = {Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976)}, pages = {53--61. Lecture Notes in Math., Vol. 601}, publisher = {Springer}, address = {Berlin}, year = {1977} } @Book{ katzmazur, author = {Katz, N.\thinspace{}M. and Mazur, B.}, title = {Arithmetic moduli of elliptic curves}, publisher = {Princeton University Press}, address = {Princeton, N.J.}, year = {1985}, pages = {xiv+514}, isbn = {0-691-08349-5, 0-691-08352-5} } @Article{ khare:manu, author = {Khare, C.}, title = {Multiplicities of mod $p$ {G}alois representations}, journal = {Manuscripta Math.}, fjournal = {Manuscripta Mathematica}, volume = {95}, year = {1998}, number = {2}, pages = {181--188}, issn = {0025-2611}, coden = {MSMHB2}, mrclass = {11F80 (11F33 11G18)}, mrnumber = {98m:11046}, mrrevr = {Ian Kiming} } @Article{ klenke:phd, author = "Klenke, T.", title = {Modular {V}arieties and {V}isibility}, journal = {Ph.D. thesis, Harvard University}, year = {2001} } @Book{ knapp:elliptic, author = {Knapp, A.\thinspace{}W.}, title = {Elliptic curves}, publisher = {Princeton University Press}, address = {Princeton, NJ}, year = {1992}, pages = {xvi+427}, isbn = {0-691-08559-5} } @Book{ koblitz:cong, author = {Koblitz, N.}, title = {Introduction to elliptic curves and modular forms}, series = {Graduate Texts in Mathematics}, volume = {97}, publisher = {Springer-Verlag}, address = {New York}, year = {1984}, pages = {viii+248}, isbn = {0-387-96029-5}, mrclass = {11G05 (11G40 14G25 14K07)}, mrnumber = {86c:11040}, mrreviewer = {Leslie Jane Federer} } @InProceedings{ kohel-stein:ants4, author = "Kohel, D.\thinspace{}R. and Stein, W.\thinspace{}A.", title = "Component {G}roups of {Q}uotients of \protect{$J_0(N)$}", booktitle = {Proceedings of the 4th International Symposium (ANTS-IV), Leiden, Netherlands, July 2--7, 2000}, publisher = {Springer}, address = {Berlin}, year = {2000} } @Article{ kohel:computing, author = "Kohel, D.\thinspace{}R.", title = "Computing modular curves via quaternions", journal = "Fourth CANT Conference", year = 1997 } @Article{ kohel:hecke, author = "Kohel, D.\thinspace{}R.", title = "Hecke Module Structure of Quaternions", journal = "In K. 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USSR Izvestiya}, volume = {39}, year = {1992}, number = {1}, pages = {829--853} } @InCollection{ kolyvagin:euler_systems, author = {Kolyvagin, V.\thinspace{}A.}, title = {Euler systems}, booktitle = {The Grothendieck Festschrift, Vol.\ II}, pages = {435--483}, publisher = {Birkh\"auser Boston}, address = {Boston, MA}, year = {1990}, mrclass = {11R34 (11G05 11G40 11R29)}, mrnumber = {92g:11109}, mrreviewer = {Karl Rubin} } @InProceedings{ kolyvagin:mordellweil, author = {Kolyvagin, V.\thinspace{}A.}, title = {On the {M}ordell-{W}eil group and the {S}hafarevich-{T}ate group of modular elliptic curves}, booktitle = {Proceedings of the International Congress of Mathematicians, Vol.\ I, II (Kyoto, 1990)}, pages = {429--436}, publisher = {Math. Soc. Japan}, address = {Tokyo}, year = {1991}, mrclass = {11G40 (11G05 14G10)}, mrnumber = {93c:11046}, mrrevr = {John Jones} } @Article{ kolyvagin:structure_of_selmer, author = {Kolyvagin, V.\thinspace{}A.}, title = {On the structure of {S}elmer groups}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {291}, year = {1991}, number = {2}, pages = {253--259}, issn = {0025-5831}, coden = {MAANA}, mrclass = {11G05 (11G40)}, mrnumber = {93e:11073}, mrreviewer = {Massimo Bertolini} } @InCollection{ kolyvagin:structureofsha, author = {Kolyvagin, V.\thinspace{}A.}, title = {On the structure of {S}hafarevich-{T}ate groups}, booktitle = {Algebraic geometry (Chicago, IL, 1989)}, pages = {94--121}, publisher = {Springer}, address = {Berlin}, year = {1991} } @Article{ kolyvagin:subclass, author = {Kolyvagin, V. A.}, title = {Finiteness of ${E}(\mathbf{Q})$ and ${\Sha}({E},\mathbf{Q})$ for a subclass of {W}eil curves}, journal = {Izv. Akad. Nauk SSSR Ser. Mat.}, fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, volume = {52}, year = {1988}, number = {3}, pages = {522--540, 670--671}, issn = {0373-2436}, mrclass = {11G05 (11G40 14G25 14K07)}, mrnumber = {89m:11056}, mrreviewer = {Reinhard B{\"o}lling} } @Article{ kolyvagin:weil, author = {Kolyvagin, V. A.}, title = {The {M}ordell-{W}eil and {S}hafarevich-{T}ate groups for {W}eil elliptic curves}, journal = {Izv. Akad. Nauk SSSR Ser. Mat.}, fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, volume = {52}, year = {1988}, number = {6}, pages = {1154--1180, 1327}, issn = {0373-2436}, mrclass = {11G05 (11D41 11G40 14G25 14K07)}, mrnumber = {90f:11035}, mrreviewer = {Reinhard B{\"o}lling} } @Article{ kramer:largesha, author = {Kramer, K.}, title = {A family of semistable elliptic curves with large {T}ate-{S}hafarevitch groups}, journal = {Proc. Amer. Math. Soc.}, fjournal = {Proceedings of the American Mathematical Society}, volume = {89}, year = {1983}, number = {3}, pages = {379--386}, issn = {0002-9939}, coden = {PAMYAR}, mrclass = {14K07 (11G05 14G25)}, mrnumber = {85d:14059}, mrreviewer = {Reinhard B{\"o}lling} } @Book{ kubert-lang, author = {Kubert, D.\thinspace{}S. and Lang, S.}, title = {Modular units}, series = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science]}, volume = {244}, publisher = {Springer-Verlag}, address = {New York}, year = {1981}, pages = {xiii+358}, isbn = {0-387-90517-0}, mrclass = {12A45 (10D05 14G25)}, mrnumber = {84h:12009}, mrreviewer = {Roland Gillard} } @Article{ lang-tate, author = {Lang, S. and Tate, J.}, title = {Principal homogeneous spaces over abelian varieties}, journal = {Amer. J. Math.}, volume = {80}, year = {1958}, pages = {659--684} } @Book{ lang:algebra, author = {Lang, S.}, title = {Algebra}, edition = {Third}, publisher = {Addison-Wesley Publishing Co., Reading, Mass.}, year = {1993}, pages = {xv+912}, isbn = {0-201-55540-9} } @Book{ lang:ant, author = {Lang, S.}, title = {Algebraic number theory}, edition = {Second}, publisher = {Springer-Verlag}, address = {New York}, year = {1994}, pages = {xiv+357}, isbn = {0-387-94225-4} } @Article{ lang:finitefields, author = {Lang, S.}, title = {Algebraic groups over finite fields}, journal = {Amer. J. Math.}, volume = {78}, year = {1956}, pages = {555--563}, mrclass = {14.0X}, mrnumber = {19,174a}, mrreviewer = {P. Roquette} } @Book{ lang:modular, author = {Lang, S.}, title = {Introduction to modular forms}, note = {With appendixes by D. Zagier and W. Feit, Corrected reprint of the 1976 original}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1995}, pages = {x+261}, isbn = {3-540-07833-9} } @Book{ lang:nt3, author = {Lang, S.}, title = {Number theory. {I}{I}{I}}, note = {Diophantine geometry}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1991}, pages = {xiv+296}, isbn = {3-540-53004-5}, mrclass = {11Gxx (14Gxx)}, mrnumber = {93a:11048}, mrreviewer = {Joseph H. Silverman} } @InProceedings{ langlands:antwerp2, author = {Langlands, R.\thinspace{}P.}, title = {Modular forms and $\ell $-adic representations}, booktitle = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, editor = {Deligne, P. and Kuyk, W.}, pages = {361--500. Lecture Notes in Math., Vol. 349}, publisher = {Springer}, address = {Berlin}, year = {1973}, mrclass = {12A70 (10D15 14G10 22E50)}, mrnumber = {50 #7095}, mrrevr = {I. I. Pjateckii-Sapiro} } @Book{ langlands:basechange, author = {Langlands, R.\thinspace{}P.}, title = {Base change for \protect{${\rm {G}{L}}(2)$}}, publisher = {Princeton University Press}, address = {Princeton, N.J.}, year = {1980}, pages = {vii+237}, isbn = {0-691-08263-4; 0-691-08272-3} } @Article{ lenstra-oort:additive, author = {Lenstra, Jr., H. W. and Oort, F.}, title = {Abelian varieties having purely additive reduction}, journal = {J. Pure Appl. Algebra}, fjournal = {Journal of Pure and Applied Algebra}, volume = {36}, year = {1985}, number = {3}, pages = {281--298}, issn = {0022-4049}, coden = {JPAAA2}, mrclass = {14K15 (11G10 14G20)}, mrnumber = {86e:14020}, mrreviewer = {Joseph H. Silverman} } @InCollection{ lenstra-smit:explicit, author = {de Smit, B. and Lenstra, H.\thinspace{}W.,Jr.}, title = {Explicit construction of universal deformation rings}, booktitle = {Modular forms and \protect{F}ermat's last theorem (Boston, MA, 1995)}, pages = {313--326}, publisher = {Springer}, address = {New York}, year = {1997} } @Book{ lenstras:nfs, title = {The development of the number field sieve}, editor = {Lenstra, A.\thinspace{}K. and Lenstra, Jr., H.\thinspace{}W.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1993}, pages = {viii+131}, isbn = {3-540-57013-6}, mrclass = {11Yxx (11-06 11N35 11N36 11Y05 11Y40)}, mrnumber = {96m:11116}, mrreviewer = {Samuel S. Wagstaff, Jr.} } @Article{ lichtenbaum:curves, author = {Lichtenbaum, Stephen}, title = {Curves over discrete valuation rings}, journal = {Amer. J. Math.}, volume = {90}, year = {1968}, pages = {380--405}, mrclass = {14.20}, mrnumber = {37 \#6284}, mrreviewer = {J.-E. Bertin} } @Article{ lichtenbaum:duality, author = {Lichtenbaum, S.}, title = {Duality theorems for curves over \protect{$p$}-adic fields}, journal = {Invent. Math.}, volume = {7}, year = {1969}, pages = {120--136} } @Article{ lidia, title = {\protect{LiDIA: C++} number theory library}, author = {Buchmann, J.} } @Article{ livne:conductors, author = {Livn{\'e}, R.}, title = {On the conductors of mod \protect{$\ell$} \protect{G}alois representations coming from modular forms}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {31}, year = {1989}, number = {2}, pages = {133--141}, issn = {0022-314X}, coden = {JNUTA9} } @Proceedings{ lms254, title = {Galois Representations in Arithmetic Algebraic Geometry}, booktitle = {Galois Representations in Arithmetic Algebraic Geometry}, editor = {Scholl A.\thinspace{}J. and Taylor R.\thinspace{}L.}, pages = {493}, year = {1998}, publisher = {Cambridge University Press} } @Article{ lorenzini:abvarred, author = {Lorenzini, D.\thinspace{}J.}, title = "On the Jacobian of the Modular Curve \protect{$X_0(N)$}", journal = "preprint" } @Article{ lorenzini:compgrp, author = {Lorenzini, D.\thinspace{}J.}, title = {On the group of components of a \protect{N}\'eron model}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {445}, year = {1993}, pages = {109--160}, issn = {0075-4102}, coden = {JRMAA8} } @Article{ magma, author = {Bosma, W. and Cannon, J. and Playoust, C.}, title = {The {M}agma algebra system. {I}. {T}he user language}, note = {Computational algebra and number theory (London, 1993)}, journal = {J. Symbolic Comput.}, fjournal = {Journal of Symbolic Computation}, volume = {24}, year = {1997}, number = {3--4}, pages = {235--265}, issn = {0747-7171}, mrclass = {68Q40}, mrnumber = {1 484 478} } @Article{ manin:cyclo, author = {Manin, J.\thinspace{}I.}, title = {Cyclotomic fields and modular curves}, journal = {Russian Math. Surveys}, volume = {26}, year = {1971}, number = {6}, pages = {7--78} } @Article{ manin:parabolic, author = {Manin, J.\thinspace{}I.}, title = {Parabolic points and zeta functions of modular curves}, journal = {Izv. Akad. Nauk SSSR Ser. Mat.}, volume = {36}, year = {1972}, pages = {19--66}, mrclass = {14G10 (10D15 14H25)}, mrnumber = {47 \#3396}, mrrevr = {K.-B. Gundlach} } @Book{ matsumura, author = {Matsumura, H.}, title = {Commutative ring theory}, note = {Translated from the Japanese by M. Reid}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {1986}, pages = {xiv+320}, isbn = {0-521-25916-9}, mrclass = {13-01}, mrnumber = {88h:13001}, mrreviewer = {W. V. Vasconcelos} } @Article{ mazur-ribet, author = {Mazur, B. and Ribet, K.\thinspace{}A.}, title = {Two-dimensional representations in the arithmetic of modular curves}, note = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)}, journal = {Ast\'erisque}, fjournal = {Ast\'erisque}, number = {196-197}, year = {1991}, pages = {6, 215--255 (1992)}, issn = {0303-1179} } @Article{ mazur-sd, author = {Mazur, B. and Swinnerton-Dyer, P.}, title = {Arithmetic of {W}eil curves}, journal = {Invent. Math.}, volume = {25}, year = {1974}, pages = {1--61}, mrclass = {14G05 (10D05)}, mrnumber = {50 #7152}, mrrevr = {J. S. Milne} } @Article{ mazur-swinnerton-dyer:arithmetic, author = {Mazur, B. and Swinnerton-Dyer, P.}, title = {Arithmetic of {W}eil curves}, journal = {Invent. Math.}, volume = {25}, year = {1974}, pages = {1--61}, mrclass = {14G05 (10D05)}, mrnumber = {50 \#7152}, mrreviewer = {J. S. Milne} } @Article{ mazur:arithmetic_values, author = {Mazur, B.}, title = {On the arithmetic of special values of ${L}$\ functions}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {55}, year = {1979}, number = {3}, pages = {207--240}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {14G10 (10D24 12A70 14G25 14K07)}, mrnumber = {82e:14033}, mrrevr = {V. V. Shokurov} } @Article{ mazur:arizona, author = "Mazur, B.", title = "Three lectures about the arithmetic of elliptic curves.", journal = "To appear in the proceedings from the Arizona Southwest Geometry Winter School", year = 1998 } @InCollection{ mazur:deforming, author = {Mazur, B.}, title = {Deforming \protect{G}alois representations}, booktitle = {Galois groups over \protect{${\bf Q}$} (Berkeley, CA, 1987)}, pages = {385--437}, publisher = {Springer}, address = {New York}, year = {1989} } @Article{ mazur:eisenstein, author = {Mazur, B.}, title = {Modular curves and the \protect{Eisenstein} ideal}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques}, number = {47}, year = {1977}, pages = {33--186 (1978)}, issn = {0073-8301}, coden = {PMIHA6} } @Article{ mazur:infinite_fern, author = {Mazur, B.}, title = {An ``infinite fern'' in the universal deformation space of {G}alois representations}, note = {Journ\'ees Arithm\'etiques (Barcelona, 1995)}, journal = {Collect. Math.}, fjournal = {Universitat de Barcelona. Collectanea Mathematica}, volume = {48}, year = {1997}, number = {1-2}, pages = {155--193}, issn = {0010-0757}, coden = {COLMBA}, mrclass = {11F33 (11F80)}, mrnumber = {98g:11053}, mrreviewer = {Andrea Mori} } @Article{ mazur:rational, author = {Mazur, B.}, title = {Rational isogenies of prime degree (with an appendix by {D}. {G}oldfeld)}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {44}, year = {1978}, number = {2}, pages = {129--162}, issn = {0020-9910}, coden = {INVMBH} } @InCollection{ mazur:symboles, author = {Mazur, B.}, title = {Courbes elliptiques et symboles modulaires}, booktitle = {S\'eminaire Bourbaki, 24\`eme ann\'ee (1971/1972), Exp. No. 414}, pages = {277--294. Lecture Notes in Math., Vol. 317}, publisher = {Springer}, address = {Berlin}, year = {1973}, mrclass = {14K15 (14G25 10D15)}, mrnumber = {55 \#2930}, mrrevr = {Jacques Velu} } @Article{ mazur:tower, author = {Mazur, B.}, title = {Rational points of abelian varieties with values in towers of number fields}, journal = {Invent. Math.}, volume = {18}, year = {1972}, pages = {183--266} } @Article{ mazur:towers, author = {Mazur, B.}, title = {Rational points of abelian varieties with values in towers of number fields}, journal = {Invent. Math.}, volume = {18}, year = {1972}, pages = {183--266}, mrclass = {14G25 (14K15)}, mrnumber = {56 3020}, mrrevr = {J.\thinspace{}S. Milne} } @Article{ mazur:visord3, author = {Mazur, B.}, title = {Visualizing elements of order three in the {S}hafarevich-{T}ate group}, note = {Sir Michael Atiyah: a great mathematician of the twentieth century}, journal = {Asian J. Math.}, fjournal = {The Asian Journal of Mathematics}, volume = {3}, year = {1999}, number = {1}, pages = {221--232}, issn = {1093-6106}, mrclass = {11G05 (14G05)}, mrnumber = {2000g:11048}, mrreviewer = {Odile Sauzet} } @Article{ mazur:visthree, author = {Mazur, B.}, title = {Visualizing elements of order three in the {S}hafarevich-{T}ate group}, journal = {Asian J. Math.}, fjournal = {The Asian Journal of Mathematics}, volume = {3}, year = {1999}, number = {1}, pages = {221--232}, issn = {1093-6106}, mrclass = {11G05 (14G05)}, mrnumber = {2000g:11048}, mrreviewer = {Odile Sauzet} } @Article{ mazurtate:13, author = {Mazur, B. and Tate, J.}, title = {Points of order $13$ on elliptic curves}, journal = {Invent. Math.}, volume = {22}, year = {1973/74}, pages = {41--49}, mrclass = {14G05 (14H40 14K15)}, mrnumber = {50 \#327}, mrreviewer = {F. Oort} } @Article{ mccallum:duality, author = {McCallum, W.\thinspace{}G.}, title = {Duality theorems for {N}\'eron models}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {53}, year = {1986}, number = {4}, pages = {1093--1124}, issn = {0012-7094}, coden = {DUMJAO}, mrclass = {14K15 (11G10 14F20)}, mrnumber = {88c:14062}, mrreviewer = {Gerd Faltings} } @InCollection{ mccallum:kolyvagin, author = {McCallum, W.\thinspace{}G.}, title = {Kolyvagin's work on {S}hafarevich-{T}ate groups}, booktitle = {$L$-functions and arithmetic (Durham, 1989)}, pages = {295--316}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, year = {1991}, mrclass = {11G40 (11G05 14G10)}, mrnumber = {92m:11062}, mrreviewer = {John Jones} } @Article{ merel-stein, author = {Merel, L. and Stein, W.\thinspace{}A.}, title = {The field generated by the points of small prime order on an elliptic curve}, journal = {Internat. Math. Res. Notices}, fjournal = {International Mathematics Research Notices}, year = {2001}, number = {20}, pages = {1075--1082}, issn = {1073-7928}, mrclass = {11G05}, mrnumber = {1 857 596} } @InProceedings{ merel:1585, author = {Merel, L.}, title = {Universal \protect{F}ourier expansions of modular forms}, booktitle = {On {A}rtin's conjecture for odd 2-dimensional representations}, pages = {59--94}, publisher = {Springer}, year = {1994} } @Article{ merel:cyclo, author = {Merel, L.}, title = {Sur la nature non-cyclotomique des points d'ordre fini des courbes elliptiques}, note = {With an appendix by E. Kowalski and P. Michel}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {110}, year = {2001}, number = {1}, pages = {81--119}, issn = {0012-7094}, coden = {DUMJAO}, mrclass = {11G05 (11G40 11L40)}, mrnumber = {2002k:11080}, mrreviewer = {Matthew H. Baker} } @Article{ merel:intersections, author = {Merel, L.}, title = {Intersections sur des courbes modulaires}, journal = {Manuscripta Math.}, fjournal = {Manuscripta Mathematica}, volume = {80}, year = {1993}, number = {3}, pages = {283--289}, issn = {0025-2611}, coden = {MSMHB2}, mrclass = {14G35 (11G18)}, mrnumber = {94k:14014}, mrreviewer = {Douglas L. Ulmer} } @Article{ merel:weil, author = {Merel, L.}, title = {L'accouplement de {W}eil entre le sous-groupe de {S}himura et le sous-groupe cuspidal de ${J}\sb 0(p)$}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {477}, year = {1996}, pages = {71--115}, issn = {0075-4102}, coden = {JRMAA8}, mrclass = {11G18 (11F67)}, mrnumber = {97f:11045}, mrrevr = {Jan Nekov{\'a}{\v{r}}} } @Article{ mestre-oesterle, author = {Mestre, J.-F. and Oesterl{\'e}, J.}, title = {Method of graphs (unpublished manuscript)} } @Article{ mestre-oesterle:crelle, author = {Mestre, J.-F. and Oesterl{\'e}, J.}, title = {Courbes de {W}eil semi-stables de discriminant une puissance \protect{$m$}-i\`eme}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {400}, year = {1989}, pages = {173--184}, issn = {0075-4102}, coden = {JRMAA8}, mrclass = {11G18 (11F70 11G05 14G25 14K07)}, mrnumber = {90g:11078}, mrrevr = {Noriko Yui} } @Article{ mestre:graphs, author = {Mestre, J.-F.}, title = {La m\'ethode des graphes. \protect{Exemples} et applications}, journal = {Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata)}, pages = {217--242}, publisher = {Nagoya Univ.}, address = {Nagoya}, year = {1986} } @Article{ mfd, author = {Stein, W.}, title = {The {M}odular {F}orms {D}atabase\\ {\tt http://modular.math.washington.edu/Tables}}, year = {2004} } @Article{ mfd2, author = {Stein, W.}, title = {The {ZOPE} {M}odular {F}orms {D}atabase}, year = {2004}, journal = {\newline{\tt http://modular.math.washington.edu/mfd}} } @InCollection{ milne:abvars, author = {Milne, J.\thinspace{}S.}, title = {Abelian varieties}, booktitle = {Arithmetic geometry (Storrs, Conn., 1984)}, pages = {103--150}, publisher = {Springer}, address = {New York}, year = {1986} } @Article{ milne:bsdres, author = {Milne, J.\thinspace{}S.}, title = {On the arithmetic of abelian varieties}, journal = {Invent. Math.}, volume = {17}, year = {1972}, pages = {177--190}, mrclass = {14K15 (14G10 14G25)}, mrnumber = {48 \#8512}, mrreviewer = {T. Ono} } @Book{ milne:duality, author = {Milne, J.\thinspace{}S.}, title = {Arithmetic duality theorems}, publisher = {Academic Press Inc.}, address = {Boston, Mass.}, year = {1986}, pages = {x+421}, isbn = {0-12-498040-6} } @Book{ milne:etale, author = {Milne, J.\thinspace{}S.}, title = {\'{E}tale cohomology}, publisher = {Princeton University Press}, address = {Princeton, N.J.}, year = {1980}, pages = {xiii+323}, isbn = {0-691-08238-3}, mrclass = {14-02 (14F20 18F99)}, mrnumber = {81j:14002}, mrrevr = {G. Horrocks} } @Book{ miyake, author = {Miyake, T.}, title = {Modular forms}, note = {Translated from the Japanese by Yoshitaka Maeda}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1989}, pages = {x+335}, isbn = {3-540-50268-8} } @Article{ momose-ozawa, title = {Rational points of modular curves \protect{$X_{\split}(p)$}}, author = {Momose and Ozawa}, year = 2002, journal = {Preprint} } @Proceedings{ motives, title = {Motives}, booktitle = {Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington, Seattle, Washington, July 20--August 2, 1991}, editor = {Jannsen, Uwe and Kleiman, Steven and Serre, Jean-Pierre}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {1994}, pages = {xiv+747}, isbn = {0-8218-1636-5}, mrclass = {11-06 (19-06)}, mrnumber = {94i:11003} } @Book{ mr, title = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69}, note = {Lecture Notes in Mathematics, Vol. 179}, publisher = {Springer-Verlag}, address = {Berlin and New York}, year = {1971} } @Book{ mr2000a:11005, title = {Galois representations in arithmetic algebraic geometry}, editor = {Scholl, A. J. and Taylor, R. L.}, note = {Papers from the London Mathematical Society Symposium held in Durham, July 9--18, 1996}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {1998}, pages = {viii+493}, isbn = {0-521-64419-4}, mrclass = {11-06}, mrnumber = {2000a:11005} } @Proceedings{ mr2000c:11002, title = {Automorphic forms, automorphic representations, and arithmetic}, booktitle = {Proceedings of the NSF-CBMS Regional Conference in Mathematics on Euler Products and Eisenstein Series held at Texas Christian University, Fort Worth, TX, May 20--24, 1996}, editor = {Doran, Robert S. and Dou, Ze-Li and Gilbert, George T.}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {1999}, pages = {xii+278}, isbn = {0-8218-0659-9}, mrclass = {11-06 (11Fxx)}, mrnumber = {2000c:11002} } @Proceedings{ mr2000g:11002, title = {Algorithmic number theory}, booktitle = {Proceedings of the 3rd International Symposium (ANTS-III) held at Reed College, Portland, OR, June 21--25, 1998}, editor = {Buhler, J. P.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1998}, pages = {x+640}, isbn = {3-540-64657-4}, mrclass = {11-06 (11Yxx)}, mrnumber = {2000g:11002} } @Proceedings{ mr2000g:11002, title = {Algorithmic number theory}, booktitle = {Proceedings of the 4th International Symposium (ANTS-IV), Leiden, The Netherlands, July 2--7, 2000}, editor = {Wieb Bosma}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2000}, pages = {}, isbn = {3540676953} } @Book{ mr2000m:11002, author = {Coates, J. and Greenberg, R. and Ribet, K. A. and Rubin, K.}, title = {Arithmetic theory of elliptic curves}, series = {Lecture Notes in Mathematics}, volume = {1716}, note = {Lectures from the 3rd C.I.M.E.\ Session held in Cetraro, July 12--19, 1997, Edited by C. Viola}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1999}, pages = {viii+234}, isbn = {3-540-66546-3}, mrclass = {11-06 (11G05)}, mrnumber = {2000m:11002} } @Book{ mr2000m:11002, author = {Coates, J. and Greenberg, R. and Ribet, K. A. and Rubin, K.}, title = {Arithmetic theory of elliptic curves}, note = {Lectures from the 3rd C.I.M.E.\ Session held in Cetraro, July 12--19, 1997, Edited by C. Viola}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1999}, pages = {viii+234}, isbn = {3-540-66546-3}, mrclass = {11-06 (11G05)}, mrnumber = {2000m:11002} } @Book{ mr2002d:11003, title = {Arithmetic algebraic geometry}, series = {IAS/Park City Mathematics Series}, volume = {9}, editor = {Conrad, Brian and Rubin, Karl}, note = {Including papers from the Graduate Summer School of the Institute for Advanced Study/Park City Mathematics Institute held in Park City, UT, June 20--July 10, 1999}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {2001}, pages = {xiv+569}, isbn = {0-8218-2173-3}, mrclass = {11-06 (14-06)}, mrnumber = {2002d:11003} } @Book{ mr35:6500, title = {Algebraic number theory}, booktitle = {Proceedings of an instructional conference organized by the London Mathematical Society (a NATO Advanced Study Institute) with the support of the Inter national Mathematical Union. Edited by J. W. S. Cassels and A. Fr\"ohlich}, publisher = {Academic Press}, address = {London}, year = {1967}, pages = {xviii+366} } @Book{ mr37:3885, title = {Proceedings of a {C}onference on {L}ocal {F}ields}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1967}, pages = {v+214}, mrclass = {00.04 (12.00)}, mrnumber = {37 \#3885} } @Book{ mr48:2080, title = {Modular functions of one variable. {I}{I}{I}}, booktitle = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, editor = {Kuyk, Willem and Serre, J.-P.}, note = {Lecture Notes in Mathematics, Vol. 350}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {iv+350}, mrclass = {10D05 (14K22)}, mrnumber = {48 #2080} } @Book{ mr48:2080, title = {Modular functions of one variable. {I}{I}{I}}, booktitle = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, editor = {Kuyk, W. and Serre, J-P.}, note = {Lecture Notes in Mathematics, Vol. 350}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {iv+350} } @Book{ mr48:5967, title = {Analytic number theory}, booktitle = {Proceedings of Symposia in Pure Mathematics, Vol. XXIV}, editor = {Diamond, Harold G.}, publisher = {American Mathematical Society}, address = {Providence, R.I.}, year = {1973}, pages = {xii+340}, mrclass = {10-06}, mrnumber = {48 \#5967} } @Book{ mr48:5967, title = {Analytic number theory}, booktitle = {Proceedings of Symposia in Pure Mathematics, Vol. XXIV}, editor = {Diamond, Harold G.}, publisher = {American Mathematical Society}, address = {Providence, R.I.}, year = {1973}, pages = {xii+340}, mrclass = {10-06}, mrnumber = {48 \#5967} } @Book{ mr48:8389, title = {Modular functions of one variable. {I}{I}}, booktitle = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, editor = {Deligne, P. and Kuyk, W.}, note = {Lecture Notes in Mathematics, Vol. 349}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {iv+598} } @Book{ mr49:6, title = {Prospects in mathematics}, booktitle = {Proceedings of a Symposium, Princeton University, Princeton, N. J., 16--18 March 1970}, note = {Annals of Mathematics Studies, No. 70}, publisher = {Princeton University Press}, address = {Princeton, N.J.}, year = {1971}, pages = {vii+185}, mrclass = {00A10}, mrnumber = {49 \#6} } @Proceedings{ mr50:16, title = {S\'eminaire Bourbaki}, booktitle = {S\'eminaire Bourbaki, 24\`eme ann\'ee (1971/1972), Exp. No. 414}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {iv+361}, mrclass = {00A10}, mrnumber = {50 #16} } @Book{ mr50:16, title = {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No. 416}, note = {Vol. 1971/1972, 24e ann\'ee: Expos\'es Nos. 400--417, Lecture Notes in Mathematics, Vol. 317}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {iv+361}, mrclass = {00A10}, mrnumber = {50 #16} } @Book{ mr50:4458, title = {Seminar on {M}odern {M}ethods in {N}umber {T}heory}, note = {Held at the Institute of Statistical Mathematics, Tokyo, August 30--September 4, 1971}, publisher = {Institute of Statistical Mathematics}, address = {Tokyo}, year = {1971}, pages = {iii+291 pp. (not consecutively paged)}, mrclass = {10-06}, mrnumber = {50 #4458} } @Book{ mr52:8007, title = {S\'eminaire de {T}h\'eorie des {N}ombres. 1971--1972}, note = {Tenu \`a l'Universit\'e de Bordeaux I, Talence, ann\'ee universitaire 1971--1972}, publisher = {Laboratoire de Th\'eorie des Nombres, Centre National de Recherche Scientifique, Talence}, year = {1972}, pages = {224 pp. (not consecutively paged)} } @Book{ mr56:11675, title = {Number theory and algebra}, editor = {Zassenhaus, H.}, note = {Collected papers dedicated to Henry B. Mann, Arnold E. Ross, and Olga Taussky-Todd}, publisher = {Academic Press [Harcourt Brace Jovanovich Publishers]}, address = {New York}, year = {1977}, pages = {x1vi+393}, isbn = {0-12-776350-3.} } @Proceedings{ mr82d:10006, title = {Theory of numbers}, series = {Proceedings of Symposia in Pure Mathematics}, booktitle = {Proceedings of the Symposium in Pure Mathematics, VIII}, editor = {Whiteman, Albert Leon}, note = {Corrected reprint of the 1965 original}, publisher = {American Mathematical Society}, address = {Providence, R.I.}, year = {1979}, pages = {vii+216}, isbn = {0-8218-1408-7}, mrclass = {10-06}, mrnumber = {82d:10006} } @Book{ mr82j:10004, title = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1979--80}, series = {Progress in Mathematics}, volume = {12}, editor = {Bertin, Marie-Jos{\'e}}, note = {S\'eminaire Delange-Pisot-Poitou. [Delange-Pisot-Poitou Seminar], Held in Paris, 1979--80}, publisher = {Birkh\"auser Boston}, address = {Mass.}, year = {1981}, pages = {ix+394}, isbn = {3-7643-3035-X}, mrclass = {10-06}, mrnumber = {82j:10004} } @Proceedings{ mr86e:00018, title = {Arbeitstagung {B}onn 1984}, booktitle = {Proceedings of the 25th mathematical workshop held at the Max-Planck-Institut f\"ur Mathematik, Bonn, June 15--22, 1984}, editor = {Hirzebruch, F. and Schwermer, J. and Suter, S.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1985}, pages = {iii+481}, isbn = {3-540-15195-8} } @Proceedings{ mr86g:00010, title = {Proceedings of the international congress of mathematicians. {V}ol. 1, 2}, editor = {Ciesielski, Zbigniew and Olech, Czes{\l}aw}, note = {Held in Warsaw, August 16--24, 1983}, publisher = {PWN---Polish Scientific Publishers}, address = {Warsaw}, year = {1984}, pages = {lxii+1730}, isbn = {83-01-05523-5} } @Proceedings{ mr87m:11004, title = {Number theory}, booktitle = {Proceedings of the seminar held at the City University of New York, New York, 1984--1985}, editor = {Chudnovsky, D.\thinspace{}V. and Chudnovsky, G.\thinspace{}V. and Cohn, H. and Nathanson, M.\thinspace{}B.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1987}, pages = {vi+324}, isbn = {3-540-17669-1} } @Proceedings{ mr88c:14001, title = {Current trends in arithmetical algebraic geometry}, booktitle = {Proceedings of the AMS-IMS-SIAM joint summer research conference held at Humboldt State University, Arcata, Calif., August 18--24, 1985}, editor = {Ribet, Kenneth A.}, publisher = {American Mathematical Society}, address = {Providence, R.I.}, year = {1987}, pages = {x+293}, isbn = {0-8218-5070-1} } @Book{ mr89b:14029, title = {Arithmetic geometry}, editor = {Cornell, G. and Silverman, J.\thinspace{}H.}, note = {Papers from the conference held at the University of Connecticut, Storrs, Conn., July 30--August 10, 1984}, publisher = {Springer-Verlag}, address = {New York}, year = {1986}, pages = {xvi+353}, isbn = {0-387-96311-1} } @Book{ mr89b:14029, title = {Arithmetic geometry}, editor = {Cornell, Gary and Silverman, Joseph H.}, note = {Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30--August 10, 1984}, publisher = {Springer-Verlag}, address = {New York}, year = {1986}, pages = {xvi+353}, isbn = {0-387-96311-1}, mrclass = {14Gxx (11D41 11Gxx 14G25 14K15)}, mrnumber = {89b:14029}, mrreviewer = {H. Gillet} } @Proceedings{ mr90b:11003, title = {Number theory}, booktitle = {Proceedings of the Fifteenth Journ\'ees Arithm\'etiques held at the University of Ulm, Ulm, September 14--18, 1987}, editor = {Schlickewei, H. P. and Wirsing, E.}, publisher = {Springer-Verlag}, address = {New York}, year = {1989}, pages = {vi+266}, isbn = {0-387-51397-3} } @Proceedings{ mr90h:14001, title = {Arithmetic of complex manifolds}, booktitle = {Proceedings of the conference held at the University of Erlangen, Erlangen, May 27--31, 1988}, editor = {Barth, W. P. and Lange, H.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1989}, pages = {vi+171}, isbn = {3-540-51729-4} } @Book{ mr90j:11004, title = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1987--88}, editor = {Goldstein, Catherine}, note = {Papers from the seminar held in Paris, 1987--88}, publisher = {Birkh\"auser Boston Inc.}, address = {Boston, MA}, year = {1990}, pages = {viii+350}, isbn = {0-8176-3458-4} } @Book{ mr91h:00035, title = {The \protect{G}rothendieck \protect{F}estschrift. \protect{V}ol. \protect{I}}, editor = {Cartier, P. and Illusie, L. and Katz, N.\thinspace{}M. and Laumon, G. and Manin, Yu. and Ribet, K.\thinspace{}A.}, note = {A collection of articles written in honor of the 60th birthday of Alexander Grothendieck}, publisher = {Birkh\"auser Boston Inc.}, address = {Boston, MA}, year = {1990}, pages = {xx+498}, isbn = {0-8176-3427-4} } @Proceedings{ mr91k:11003, title = {$L$-functions and arithmetic}, booktitle = {Proceedings of the London Mathematical Society Symposium held at the University of Durham, Durham, June 30--July 11, 1989}, editor = {Coates, J. and Taylor, M. J.}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {1991}, pages = {ix+392}, isbn = {0-521-38619-5} } @Book{ mr92b:00051, title = {The {G}rothendieck {F}estschrift. {V}ol. {I}{I}}, editor = {Cartier, P. and Illusie, L. and Katz, N. M. and Laumon, G. and Ribet, K. A.}, note = {A collection of articles written in honor of the 60th birthday of Alexander Grothendieck}, publisher = {Birkh\"auser Boston Inc.}, address = {Boston, MA}, year = {1990}, pages = {viii+563}, isbn = {0-8176-3428-2}, mrclass = {00B30 (11-06 14-06)}, mrnumber = {92b:00051} } @Proceedings{ mr92i:11131, title = {Computational number theory}, booktitle = {Proceedings of the colloquium held at Kossuth Lajos University, Debrecen, September 4--9, 1989}, editor = {Peth{\H{o}}, Attila and Pohst, Michael E. and Williams, Hugh C. and Zimmer, Horst G{\"u}nter}, publisher = {Walter de Gruyter \& Co.}, address = {Berlin}, year = {1991}, pages = {xiv+342}, isbn = {3-11-012394-0}, mrclass = {11Yxx (11-06)}, mrnumber = {92i:11131} } @Proceedings{ mr93d:14004, title = {Algebraic geometry}, booktitle = {Proceedings of the US-USSR Symposium held at the University of Chicago, Chicago, Illinois, June 20--July 14, 1989}, editor = {Bloch, S. and Dolgachev, I. and Fulton, W.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1991}, pages = {viii+300}, isbn = {3-540-54456-9} } @Proceedings{ mr93k:00030, title = {Algebra and topology 1992}, booktitle = {Proceedings of the Seventh KAIST Mathematics Workshop held in Taej\u on, August 11--14, 1992}, editor = {Hahn, S. G. and Suh, D. Y.}, publisher = {Korea Advanced Institute of Science and Technology Mathematics Research Center}, address = {Taej\u on}, year = {1992}, pages = {x+271}, mrclass = {00B25}, mrnumber = {93k:00030} } @Book{ mr94m:11006, title = {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer conjecture}, editor = {Mazur, Barry and Stevens, Glenn}, note = {Papers from the workshop held at Boston University, Boston, Massachusetts, August 12--16, 1991}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {1994}, pages = {xiv+315}, isbn = {0-8218-5180-2}, mrclass = {11-06 (11G40)}, mrnumber = {94m:11006} } @Book{ mr95i:11001, title = {On {A}rtin's conjecture for odd 2-dimensional representations}, editor = {Frey, G.}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1994}, pages = {viii+148}, isbn = {3-540-58387-4}, mrclass = {11-06 (11F80)}, mrnumber = {95i:11001}, note = {1585} } @Proceedings{ mr95j:11119, title = {Algorithmic number theory}, booktitle = {Proceedings of the First International Symposium (ANTS-I) held at Cornell University, Ithaca, New York, May 6--9, 1994}, editor = {Adleman, Leonard M. and Huang, Ming-Deh}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1994}, pages = {x+323}, isbn = {3-540-58691-1} } @Book{ mr96f:11004, title = {Seminar on {F}ermat's {L}ast {T}heorem}, editor = {Murty, V. Kumar}, note = {Papers from the seminar held at the Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, 1993--1994}, publisher = {Published by the American Mathematical Society, Providence, RI}, year = {1995}, pages = {x+265}, isbn = {0-8218-0313-1}, mrclass = {11-06 (11D41 11G05 11G18)}, mrnumber = {96f:11004} } @Proceedings{ mr98g:11001, title = {Computational perspectives on number theory}, booktitle = {Proceedings of the conference in honor of A. O. L. Atkin held at the University of Illinois, Chicago, IL, September 1995}, editor = {Buell, D. A. and Teitelbaum, J. T.}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {1998}, pages = {x+232}, isbn = {0-8218-0880-X}, mrclass = {11-01 (00B30 11Yxx)}, mrnumber = {98g:11001} } @Proceedings{ mr98g:11001, title = {Computational perspectives on number theory}, booktitle = {Proceedings of the conference in honor of A. O. L. Atkin held at the University of Illinois, Chicago, IL, September 1995}, editor = {Buell, D. A. and Teitelbaum, J. T.}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {1998}, pages = {x+232}, isbn = {0-8218-0880-X} } @Book{ mr99f:00041, title = {S\'eminaire {B}ourbaki. {V}ol. 9}, note = {Ann\'ees 1964/65-1965/66. [Years 1964/65-1965/66], Expos\'es 277--312, Reprint of the edition published by W. A. Benjamin, New York-Amsterdam, 1966 [MR {\bf 33} \#5420l; MR {\bf 34} \#5605]}, publisher = {Soci\'et\'e Math\'ematique de France}, address = {Paris}, year = {1995}, pages = {iv+531}, isbn = {2-85629-042-6} } @Proceedings{ mr99m:11004, title = {Topics in number theory}, series = {Mathematics and its Applications}, volume = {467}, booktitle = {Proceedings of the conference held at the Pennsylvania State University, University Park, PA, July 31--August 3, 1997}, editor = {Ahlgren, Scott D. and Andrews, George E. and Ono, Ken}, note = {In honor of B. Gordon and S. Chowla}, publisher = {Kluwer Academic Publishers}, address = {Dordrecht}, year = {1999}, pages = {viii+258}, isbn = {0-7923-5583-0}, mrclass = {11-06}, mrnumber = {99m:11004} } @Book{ mumford:abvars, author = {Mumford, D.}, title = {Abelian varieties}, note = {Tata Institute of Fundamental Research Studies in Mathematics, No. 5 }, publisher = {Published for the Tata Institute of Fundamental Research, Bombay}, year = {1970}, pages = {viii+242} } @Book{ mumford:geometric, author = {Mumford, D. and Fogarty, J. and Kirwan, F.}, title = {Geometric invariant theory}, edition = {Third}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1994}, pages = {xiv+292}, isbn = {3-540-56963-4} } @article {murty-murty:mean, AUTHOR = {Murty, M. Ram and Murty, V. Kumar}, TITLE = {Mean values of derivatives of modular {$L$}-series}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {133}, YEAR = {1991}, NUMBER = {3}, PAGES = {447--475}, ISSN = {0003-486X}, CODEN = {ANMAAH}, MRCLASS = {11F67 (11G05 11G40)}, MRNUMBER = {MR1109350 (92e:11050)}, MRREVIEWER = {Daniel Bump}, } @Book{ murty-murty, author = {Murty, M.\thinspace{}R. and Murty, V.\thinspace{}K.}, title = {Non-vanishing of ${L}$-functions and applications}, publisher = {Birkh\"auser Verlag}, address = {Basel}, year = {1997}, pages = {xii+196}, isbn = {3-7643-5801-7} } @InCollection{ murty:congruence, author = {Murty, M.\thinspace{}R.}, title = {Bounds for congruence primes}, booktitle = {Automorphic forms, automorphic representations, and arithmetic (Fort Worth, TX, 1996)}, pages = {177--192}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1999}, mrclass = {11F66 (11G05)}, mrnumber = {2000g:11038}, mrrevr = {Alexey A. Panchishkin} } @Article{ mwrank, author = {Cremona, J.\thinspace{}E.}, title = {{\tt mwrank} (computer software)}, journal = {\\{\tt http://www.maths.nott.ac.uk/personal/jec/ftp/progs/}} } @Article{ neron, author = {N{\'e}ron, A.}, title = {Mod\`eles minimaux des vari\'et\'es ab\'eliennes sur les corps locaux et globaux}, journal = {Inst. Hautes \'Etudes Sci. Publ.Math. No.}, volume = {21}, year = {1964}, pages = {128}, mrclass = {14.49 (14.51)}, mrnumber = {31 \#3423}, mrreviewer = {M. Artin} } @Book{ neronmodels, author = {Bosch, S. and L{\"u}tkebohmert, W. and Raynaud, M.}, title = {N\'eron models}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1990}, pages = {x+325}, isbn = {3-540-50587-3}, mrclass = {14K15 (11G10 14L15)}, mrnumber = {91i:14034}, mrrevr = {J. Milne} } @Article{ neumann1, author = {Neumann, O.}, title = {Elliptische {K}urven mit vorgeschriebenem {R}eduktionsverhalten. {I}}, journal = {Math. Nachr.}, volume = {49}, year = {1971}, pages = {107--123}, mrclass = {14K15 (14G25)}, mrnumber = {49 \#2767a}, mrreviewer = {J. W. S. Cassels} } @Article{ neumann2, author = {Neumann, O.}, title = {Elliptische {K}urven mit vorgeschriebenem {R}eduktionsverhalten. {I}{I}}, journal = {Math. Nachr.}, volume = {56}, year = {1973}, pages = {269--280}, mrclass = {14K15 (14G25)}, mrnumber = {49 \#2767b}, mrreviewer = {J. W. S. Cassels} } @Article{ ntl, title = {\protect{NTL: Number} theory library}, author = {Shoup, V.} } @Article{ ogg:hyperelliptic, author = {Ogg, Andrew P.}, title = {Hyperelliptic modular curves}, journal = {Bull. Soc. Math. France}, volume = {102}, year = {1974}, pages = {449--462}, mrclass = {14G05 (10D05 14H45)}, mrnumber = {51 \#514}, mrreviewer = {Kuang-yen Shih} } @InCollection{ ogg:rational13, author = {Ogg, A. P.}, title = {Rational points on certain elliptic modular curves}, booktitle = {Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV, St. Louis Univ., St. Louis, Mo., 1972)}, pages = {221--231}, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, year = {1973}, mrclass = {14G05 (10D05 14K15)}, mrnumber = {49 \#2743}, mrreviewer = {J. W. S. Cassels} } @InCollection{ ogg:rationalpoints, author = {Ogg, A. P.}, title = {Rational points on certain elliptic modular curves}, booktitle = {Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV, St. Louis Univ., St. Louis, Mo., 1972)}, pages = {221--231}, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, year = {1973}, mrclass = {14G05 (10D05 14K15)}, mrnumber = {49 \#2743}, mrreviewer = {J. W. S. Cassels} } @Article{ ogg:ratpoints_finiteorder, author = {Ogg, A.\thinspace{}P.}, title = {Rational points of finite order on elliptic curves}, journal = {Invent. Math.}, volume = {12}, year = {1971}, pages = {105--111}, mrclass = {10D05}, mrnumber = {45 \#178}, mrreviewer = {K. Mahler} } @InCollection{ ogg:ratpoints_oncertain, author = {Ogg, A. P.}, title = {Rational points on certain elliptic modular curves}, booktitle = {Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV, St. Louis Univ., St. Louis, Mo., 1972)}, pages = {221--231}, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, year = {1973}, mrclass = {14G05 (10D05 14K15)}, mrnumber = {49 \#2743}, mrreviewer = {J. W. S. Cassels} } @Article{ ono-mcgraw, title = {Modular form Congruences and Selmer groups}, author = {Ono, K. and McGraw W.}, year = {2002}, journal = {Preprint} } @Article{ ono:partition, author = {Ono, K. and Guo, L.}, title = {The partition function and the arithmetic of certain modular \protect{$L$}-functions}, journal = {International Mathematical Research Notes}, number = {}, year = {1999}, pages = {} } @Article{ pentium, author = {Edelman, A.}, title = {The mathematics of the {P}entium division bug}, journal = {SIAM Rev.}, fjournal = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, volume = {39}, year = {1997}, number = {1}, pages = {54--67}, issn = {0036-1445}, coden = {SIREAD}, mrclass = {68M07}, mrnumber = {98a:68009}, mrreviewer = {Behrooz Parhami} } @Article{ pizer:alg, author = {Pizer, A.}, title = {An algorithm for computing modular forms on \protect{$\Gamma\sb{0}({N})$}}, journal = {J. Algebra}, fjournal = {Journal of Algebra}, volume = {64}, year = {1980}, number = {2}, pages = {340--390}, issn = {0021-8693}, coden = {JALGA4} } @Article{ pizer:arithmetic, author = {Pizer, A.}, title = {On the arithmetic of quaternion algebras}, journal = {Acta Arith.}, volume = {31}, year = {1976}, number = {1}, pages = {61--89} } @Article{ pizer:arithmetictwo, author = {Pizer, A.}, title = {On the arithmetic of quaternion algebras. \protect{II}}, journal = {J. Math. Soc. Japan}, volume = {28}, year = {1976}, number = {4}, pages = {676--688} } @Article{ pizer:rep, author = {Pizer, A.}, title = {The representability of modular forms by theta series}, journal = {J. Math. Soc. Japan}, volume = {28}, year = {1976}, number = {4}, pages = {689--698} } @Article{ poonen-schaefer, author = {Poonen, B. and Schaefer, E.\thinspace{}F.}, title = {Explicit descent for {J}acobians of cyclic covers of the projective line}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {488}, year = {1997}, pages = {141--188}, issn = {0075-4102}, coden = {JRMAA8}, mrclass = {11G30 (11G10 14H30 14H40)}, mrnumber = {98k:11087}, mrreviewer = {David Grant} } @Article{ poonen-stoll, author = {Poonen, B. and Stoll, M.}, title = {The {C}assels-{T}ate pairing on polarized abelian varieties}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {150}, year = {1999}, number = {3}, pages = {1109--1149}, issn = {0003-486X}, coden = {ANMAAH}, mrclass = {11G10 (11G30 14H40 14K15)}, mrnumber = {2000m:11048}, mrreviewer = {Tam{\'a}s Szamuely} } @Article{ pyle:thesis, author = {Pyle, E.}, title = {Abelian varieties over {$\Q$} with large endomorphism algebras and their simple components over {$\Qbar$}}, journal = {{\tt http://math.berkeley.edu/~ribet/pyle\_thesis.pdf}} } @InProceedings{ queen, author = {Queen, C.}, title = {The existence of \protect{$p$}-adic \protect{A}belian \protect{${L}$}-functions}, booktitle = {Number theory and algebra}, pages = {263--288}, publisher = {Academic Press}, address = {New York}, year = {1977} } @Article{ rama, author = {Ramakrishna, R.}, title = {Lifting {G}alois representations}, journal = {preprint} } @Article{ ramakrishna:deform, author = {Ramakrishna, R.}, title = {Deforming an even representation}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {132}, year = {1998}, number = {3}, pages = {563--580}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11R32 (11R34)}, mrnumber = {99h:11128}, mrrevr = {Nigel Boston} } @Article{ ramakrishna:lift2, author = {Ramakrishna, R.}, title = {Deforming {G}alois representations and the conjectures of {S}erre and {F}ontaine-{M}azur}, journal = {preprint, \protect{\tt ftp://math.cornell.edu/pub/ravi}}, fjournal = {}, volume = {}, year = {2000}, number = {}, pages = {} } @Article{ ramakrishna:lifting, author = {Ramakrishna, R.}, title = {Lifting {G}alois representations}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {138}, year = {1999}, number = {3}, pages = {537--562}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11Fxx}, mrnumber = {1 719 819} } @Article{ raynaud, author = {Raynaud}, title = {I'm not sure which paper} } @Article{ raynaud:ihes, author = {Raynaud, M.}, title = {Sp\'ecialisation du foncteur de {P}icard}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math. No.}, volume = {38}, year = {1970}, pages = {27--76}, mrclass = {14.55}, mrnumber = {44 #227}, mrrevr = {R. T. Hoobler} } @Article{ raynaud:pp, author = {Raynaud, Michel}, title = {Sch\'emas en groupes de type {$(p,\dots, p)$}}, journal = {Bull. Soc. Math. France}, volume = {102}, year = {1974}, pages = {241--280}, mrclass = {14L20 (14L25)}, mrnumber = {54 \#7488}, mrreviewer = {F. Oort} } @InCollection{ ribet-stein:serre, author = {Ribet, K.\thinspace{}A. and Stein, W.\thinspace{}A.}, title = {Lectures on {S}erre's conjectures}, booktitle = {Arithmetic algebraic geometry (Park City, UT, 1999)}, series = {IAS/Park City Math. Ser.}, volume = {9}, pages = {143--232}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {2001}, mrclass = {11F80 (11F66 11G05)}, mrnumber = {2002h:11047}, mrreviewer = {Chandrashekhar Khare} } @InCollection{ ribet:abvars, author = {Ribet, K.\thinspace{}A.}, title = {Abelian varieties over {${\bf Q}$} and modular forms}, booktitle = {Algebra and topology 1992 (Taej\u on)}, pages = {53--79}, publisher = {Korea Adv. Inst. Sci. Tech.}, address = {Taej\u on}, year = {1992}, mrclass = {11G18 (11F33 14G35 14H52)}, mrnumber = {94g:11042}, mrreviewer = {Bas Edixhoven} } @InCollection{ ribet:endalg, author = {Ribet, K. A.}, title = {Endomorphism algebras of abelian varieties attached to newforms of weight {$2$}}, booktitle = {Seminar on Number Theory, Paris 1979--80}, series = {Progr. Math.}, volume = {12}, pages = {263--276}, publisher = {Birkh\"auser Boston}, address = {Mass.}, year = {1981}, mrclass = {10D15 (14G13)}, mrnumber = {82m:10044}, mrreviewer = {Wen Ch'ing Winnie Li} } @Article{ ribet:endo, author = {Ribet, K.\thinspace{}A.}, title = {Endomorphisms of semi-stable abelian varieties over number fields}, journal = {Ann. Math. (2)}, volume = {101}, year = {1975}, pages = {555--562}, mrclass = {14K15 (10D05)}, mrnumber = {51 \#8120}, mrreviewer = {M. Kuga} } @InProceedings{ ribet:galoisattached, author = {Ribet, K.\thinspace{}A.}, title = {Galois representations attached to eigenforms with \protect{N}ebentypus}, booktitle = {Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976)}, pages = {17--51. Lecture Notes in Math., Vol. 601}, publisher = {Springer}, address = {Berlin}, year = {1977} } @Article{ ribet:galoissurvey, author = {Ribet, K.\thinspace{}A.}, title = {Galois representations and modular forms}, journal = {Bull. Amer. Math. Soc. (N.S.)}, fjournal = {American Mathematical Society. Bulletin. New Series}, volume = {32}, year = {1995}, number = {4}, pages = {375--402}, issn = {0273-0979}, coden = {BAMOAD} } @Article{ ribet:lowering, author = {Ribet, K.\thinspace{}A.}, title = {Lowering the levels of modular representations without multiplicity one}, journal = {International Mathematics Research Notices}, year = {1991}, pages = {15--19} } @Article{ ribet:mestreletter, author = {Ribet, K.\thinspace{}A.}, title = {Letter to \protect{M}estre}, year = {November, 1987} } @Article{ ribet:modreps, author = {Ribet, K.\thinspace{}A.}, title = {On modular representations of \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$} arising from modular forms}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {100}, year = {1990}, number = {2}, pages = {431--476}, issn = {0020-9910}, coden = {INVMBH} } @InCollection{ ribet:raising, author = {Ribet, K.\thinspace{}A.}, title = {Raising the levels of modular representations}, booktitle = {S\'eminaire de Th\'eorie des Nombres, Paris 1987--88}, pages = {259--271}, publisher = {Birkh\"auser Boston}, address = {Boston, MA}, year = {1990} } @InCollection{ ribet:report, author = {Ribet, K.\thinspace{}A.}, title = {Report on mod \protect{$\ell$} representations of \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$}}, booktitle = {Motives (Seattle, WA, 1991)}, pages = {639--676}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1994} } @InCollection{ ribet:torsion, author = {Ribet, K.\thinspace{}A.}, title = {Torsion points on ${J}\sb 0({N})$ and {G}alois representations}, booktitle = {Arithmetic theory of elliptic curves (Cetraro, 1997)}, pages = {145--166}, publisher = {Springer}, address = {Berlin}, year = {1999}, mrclass = {11G18 (11F80)}, mrnumber = {2001b:11054}, mrreviewer = {Matthew H. Baker} } @InCollection{ ribet:torsionj0, author = {Ribet, K.\thinspace{}A.}, title = {Torsion points on {$J\sb 0(N)$} and {G}alois representations}, booktitle = {Arithmetic theory of elliptic curves (Cetraro, 1997)}, series = {Lecture Notes in Math.}, volume = {1716}, pages = {145--166}, publisher = {Springer}, address = {Berlin}, year = {1999}, mrclass = {11G18 (11F80)}, mrnumber = {2001b:11054}, mrreviewer = {Matthew H. Baker} } @Article{ ribet:toulouse, author = {Ribet, K.\thinspace{}A.}, title = {From the \protect{T}aniyama-\protect{S}himura conjecture to \protect{F}ermat's last theorem}, journal = {Ann. Fac. Sci. Toulouse Math. (5)}, fjournal = {Toulouse. Facult\'e des Sciences. Annales. Math\'ematiques. S\'erie 5}, volume = {11}, year = {1990}, number = {1}, pages = {116--139}, issn = {0240-2955} } @Article{ ribet:twistsendoalg, author = {Ribet, K.\thinspace{}A.}, title = {Twists of modular forms and endomorphisms of abelian varieties}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {253}, year = {1980}, number = {1}, pages = {43--62}, issn = {0025-5831}, coden = {MAANA3}, mrclass = {10D15 (14G13)}, mrnumber = {82e:10043}, mrreviewer = {Wen Ch'ing Winnie Li} } @Book{ robert:elliptic, author = {Robert, A.}, title = {Elliptic curves}, note = {Notes from postgraduate lectures given in Lausanne 1971/72, Lecture Notes in Mathematics, Vol. 326}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {viii+264}, mrclass = {14K15}, mrnumber = {50 #4594}, mrrevr = {Kuang-yen Shih} } @Article{ rohrlich:cyclo, author = {Rohrlich, D.\thinspace{}E.}, title = {On {$L$}-functions of elliptic curves and cyclotomic towers}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {75}, year = {1984}, number = {3}, pages = {409--423}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11G40 (11R23 14G10)}, mrnumber = {86g:11038b}, mrreviewer = {Karl Rubin} } @InCollection{ rosen:abvars, author = {Rosen, M.}, title = {Abelian varieties over \protect{${\bf {C}}$}}, booktitle = {Arithmetic geometry (Storrs, Conn., 1984)}, pages = {79--101}, publisher = {Springer}, address = {New York}, year = {1986} } @Book{ rubin:book, author = {Rubin, K.}, title = {{E}uler {S}ystems}, note = {{A}nnals of {M}athematics {S}tudies {\bf 147}, \protect{\tt http://math.Stanford.EDU/\~{ }rubin/weyl.html}}, publisher = {Princeton University Press}, year = {Spring 2000} } @Article{ rubin:cmsha, author = {Rubin, Karl}, title = {Tate-{S}hafarevich groups and ${L}$-functions of elliptic curves with complex multiplication}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {89}, year = {1987}, number = {3}, pages = {527--559}, issn = {0020-9910}, coden = {INVMBH} } @InCollection{ rubin:kato, author = {Rubin, K.}, title = {Euler systems and modular elliptic curves}, booktitle = {Galois representations in arithmetic algebraic geometry (Durham, 1996)}, pages = {351--367}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, year = {1998}, mrclass = {11G40 (11G05 11R18 11R23)}, mrnumber = {2001a:11106}, mrreviewer = {Massimo Bertolini} } @InCollection{ rubin:kolyvagin, author = {Rubin, K.}, title = {The work of {K}olyvagin on the arithmetic of elliptic curves}, booktitle = {Arithmetic of complex manifolds (Erlangen, 1988)}, pages = {128--136}, publisher = {Springer}, address = {Berlin}, year = {1989} } @Article{ rubin:main-conjectures, author = {Rubin, K.}, title = {The ``main conjectures'' of {I}wasawa theory for imaginary quadratic fields}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {103}, year = {1991}, number = {1}, pages = {25--68}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11R23 (11G05 11G40)}, mrnumber = {92f:11151}, mrrevr = {M. A. Kenku} } @Article{ saito, author = {Saito, T.}, title = {Modular forms and \protect{$p$}-adic {H}odge theory}, journal = {Invent. Math.}, volume = {129}, year = {1997}, pages = {607--620} } @Article{ sbtaylor, author = {Shepherd-Barron, N. I. and Taylor, R.}, title = {Mod 2 and mod 5 icosahedral representations}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {10}, year = {1997}, number = {2}, pages = {283--298}, issn = {0894-0347} } @Book{ schilling, title = {Arithmetical algebraic geometry. (\protect{P}roceedings of a \protect{C}onference held at \protect{P}urdue \protect{U}niversity, \protect{D}ecember 5--7, 1963)}, editor = {Schilling, O.\thinspace{}F.\thinspace{}G.}, publisher = {Harper \& Row Publishers}, address = {New York}, year = {1965}, pages = {vii+200} } @Article{ schneider:iwasawa, author = {Schneider, P.}, title = {Iwasawa ${L}$-functions of varieties over algebraic number fields. {A} first approach}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {71}, year = {1983}, number = {2}, pages = {251--293}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11G40 (11G10 14G10 14K15)}, mrnumber = {85d:11063}, mrreviewer = {Stephen Lichtenbaum} } @InCollection{ scholl:kato, author = {Scholl, A.\thinspace{}J.}, title = {An introduction to {K}ato's {E}uler systems}, booktitle = {Galois Representations in Arithmetic Algebraic Geometry}, pages = {379--460}, year = {1998}, publisher = {Cambridge University Press} } @Article{ scholl:motivesinvent, author = {Scholl, A.\thinspace{}J.}, title = {Motives for modular forms}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {100}, year = {1990}, number = {2}, pages = {419--430}, issn = {0020-9910}, coden = {INVMBH} } @Article{ schur:arith, author = {Schur, I.}, title = {Arithmetische {U}ntersuchungen \"uber endliche {G}ruppen linearer {S}ubstitutionen}, journal = {Sitz. Pr. Akad. Wiss.}, year = {1906}, pages = {164--184}, note = {Gesam. Abhl., {\bf I}, 177--197, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1973} } @InCollection{ sd:bsd, author = {Swinnerton-Dyer, P.}, title = {The conjectures of {B}irch and {S}winnerton-{D}yer, and of {T}ate}, booktitle = {Proc. Conf. Local Fields (Driebergen, 1966)}, pages = {132--157}, publisher = {Springer}, address = {Berlin}, year = {1967}, mrclass = {14.48}, mrnumber = {37 \#6287}, mrreviewer = {Y. Nakai} } @Article{ serre-tate, author = {Serre, J-P. and Tate, J.\thinspace{}T.}, title = {Good reduction of abelian varieties}, journal = {Ann. of Math. (2)}, volume = {88}, year = {1968}, pages = {492--517} } @Book{ serre:alggroups, author = {Serre, J-P.}, title = {Algebraic groups and class fields}, note = {Translated from the French}, publisher = {Springer-Verlag}, address = {New York}, year = {1988}, pages = {x+207}, isbn = {0-387-96648-X} } @InProceedings{ serre:antwerp72, author = {Serre, J-P.}, title = {Formes modulaires et fonctions z\^eta $p$-adiques}, booktitle = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, pages = {191--268. Lecture Notes in Math., Vol. 350}, publisher = {Springer}, address = {Berlin}, year = {1973}, mrclass = {10D05}, mrnumber = {53 #7949a}, mrrevr = {K.-B. Gundlach} } @InCollection{ serre:arcata, author = {Serre, J-P.}, title = {Lettre \`a {J}.-{F}. {M}estre}, booktitle = {Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985)}, pages = {263--268}, publisher = {Amer. Math. Soc.}, address = {Providence, RI}, year = {1987} } @Book{ serre:arithmetic, author = {Serre, J-P.}, title = {A \protect{C}ourse in \protect{A}rithmetic}, note = {Translated from the French, Graduate Texts in Mathematics, No. 7}, publisher = {Springer-Verlag}, address = {New York}, year = {1973}, pages = {viii+115} } @InCollection{ serre:cnrs, author = {Serre, Jean-Pierre}, title = {Groupes de {L}ie $l$-adiques attach\'es aux courbes elliptiques}, booktitle = {Les Tendances G\'eom. en Alg\'ebre et Th\'eorie des Nombres}, pages = {239--256}, publisher = {\'Editions du Centre National de la Recherche Scientifique, Paris}, year = {1966}, mrclass = {14.50}, mrnumber = {36 #1453}, mrrevr = {H. Popp} } @Article{ serre:conjectures, author = {Serre, J-P.}, title = {Sur les repr\'esentations modulaires de degr\'e \protect{$2$} de \protect{${\rm{G}al}(\overline{\bf {Q}}/{\bf {Q}})$}}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {54}, year = {1987}, number = {1}, pages = {179--230}, issn = {0012-7094}, coden = {DUMJAO} } @InCollection{ serre:discrete, author = {Serre, J-P.}, title = {Cohomologie des groupes discrets}, booktitle = {Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970)}, pages = {77--169. Ann. of Math. Studies, No. 70}, publisher = {Princeton Univ. Press}, address = {Princeton, N.J.}, year = {1971}, mrclass = {22E40 (12A70 20G10 32N99)}, mrnumber = {52 \#5876}, mrreviewer = {H. Bass} } @Article{ serre:enseign, author = {Serre, J-P.}, title = {Divisibilit\'e de certaines fonctions arithm\'etiques}, journal = {Enseignement Math. (2)}, volume = {22}, year = {1976}, number = {3-4}, pages = {227--260}, mrclass = {10H25 (10D05)}, mrnumber = {55 #7958}, mrrevr = {Larry J. Goldstein} } @Book{ serre:gc, author = {Serre, J-P.}, title = {Galois cohomology}, note = {Translated from the French by Patrick Ion and revised by the author}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1997}, pages = {x+210}, isbn = {3-540-61990-9} } @Book{ serre:ladic, author = {Serre, J-P.}, title = {Abelian \protect{$\ell$}-adic representations and elliptic curves}, note = {With the collaboration of Willem Kuyk and John Labute, Revised reprint of the 1968 original}, publisher = {A\thinspace{}K Peters Ltd.}, address = {Wellesley, MA}, year = {1998}, pages = {199}, isbn = {1-56881-077-6} } @Book{ serre:lie_theory, author = {Serre, J-P.}, title = {Lie algebras and {L}ie groups}, series = {Lecture Notes in Mathematics}, volume = {1500}, edition = {Second}, note = {1964 lectures given at Harvard University}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1992}, pages = {viii+168}, isbn = {3-540-55008-9}, mrclass = {17-01 (17Bxx 22-01)}, mrnumber = {93h:17001} } @Book{ serre:linear, author = {Serre, J-P.}, title = {Linear representations of finite groups}, note = {Translated from the second French edition by Leonard L. Scott, Graduate Texts in Mathematics, Vol. 42}, publisher = {Springer-Verlag}, address = {New York}, year = {1977}, pages = {x+170}, isbn = {0-387-90190-6} } @InCollection{ serre:local, author = {Serre, J-P.}, title = {Local class field theory}, booktitle = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, pages = {128--161}, publisher = {Thompson, Washington, D.C.}, year = {1967} } @Book{ serre:localfields, author = {Serre, J-P.}, title = {Local fields}, note = {Translated from the French by Marvin Jay Greenberg}, publisher = {Springer-Verlag}, address = {New York}, year = {1979}, pages = {viii+241}, isbn = {0-387-90424-7} } @Book{ serre:oeuvres, author = {Serre, J-P.}, title = {{\OE}uvres. {C}ollected papers. {IV}}, note = {1985--1998}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2000}, pages = {viii+657}, isbn = {3-540-65683-9}, mrclass = {01A75 (11-03 12-03 14-03 22E50)}, mrnumber = {2001e:01037}, mrreviewer = {Alexey A. Panchishkin} } @Article{ serre:propgal, author = {Serre, J-P.}, title = {Propri\'et\'es galoisiennes des points d'ordre fini des courbes elliptiques}, journal = {Invent. Math.}, volume = {15}, year = {1972}, number = {4}, pages = {259--331} } @Article{ serre:propres, author = {Serre, J-P.}, title = {Valeurs propres des \protect{op\'{e}rateurs} de \protect{Hecke} modulo \protect{$\ell$}}, journal = {\protect{Ast\'{e}risque}}, volume = {24--25}, year = {1975}, pages = {109--117} } @Article{ serre:pseudoreflections, author = {Serre, J-P.}, title = {Groupes finis d'automorphismes d'anneaux locaux r\'eguliers}, journal = {Colloque d'Alg\`ebre (Paris, 1967), Exp. 8}, pages = {11}, publisher = {Secr\'etariat math\'ematique}, address = {Paris}, year = {1968}, mrclass = {13.95}, mrnumber = {38 \#3267}, mrreviewer = {Y. Nakai} } @Article{ serre:travauxwiles, author = {Serre, J-P.}, title = {Travaux de {W}iles (et {T}aylor, $\ldots$). {I}}, note = {S\'eminaire Bourbaki, Vol.\ 1994/95}, journal = {Ast\'erisque}, fjournal = {Ast\'erisque}, number = {237}, year = {1996}, pages = {Exp.\ No.\ 803, 5, 319--332}, issn = {0303-1179}, mrclass = {11G05 (11D41 11F80 11F85 11G18)}, mrnumber = {97m:11076}, mrreviewer = {Alexey A. Panchishkin} } @Article{ serretau, author = {Serre, J-P.}, title = {Une \protect{interpr\'etation} des congruences relatives \protect{\`a} la fonction \protect{$\tau$} de {R}amanujan}, journal = {\protect{S\'eminaire Delange-Pisot-Poitou}}, year = {1967--68}, volume = {\protect{$n^o$} 14} } @Article{ setzer, author = {Setzer, B.}, title = {Elliptic curves of prime conductor}, journal = {J. London Math. Soc. (2)}, volume = {10}, year = {1975}, pages = {367--378}, mrclass = {14K15 (10D05 14G25)}, mrnumber = {51 \#8121}, mrreviewer = {M. Basmakov} } @Book{ sga3.1, author = {Grothendieck, A.}, title = {Sch\'emas en groupes. {I}: {P}ropri\'et\'es g\'en\'erales des sch\'emas en groupes}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1970}, pages = {xv+564}, mrclass = {14.50}, mrnumber = {43 \#223a} } @Book{ sga3.2, author = {Grothendieck, A.}, title = {Sch\'emas en groupes. {I}{I}: {G}roupes de type multiplicatif, et structure des sch\'emas en groupes g\'en\'eraux}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1962/1964}, pages = {ix+654}, mrclass = {14.50}, mrnumber = {43 \#223b} } @Book{ sga3.3, author = {Grothendieck, A.}, title = {Sch\'emas en groupes. {I}{I}{I}: {S}tructure des sch\'emas en groupes r\'eductifs}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1962/1964}, pages = {viii+529}, mrclass = {14.50}, mrnumber = {43 \#223c} } @Book{ sga7.2, author = {Deligne, P. and Katz, N.}, title = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. {I}{I}}, note = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie 1967--1969 (SGA 7 II), Dirig\'e par P. Deligne et N. Katz, Lecture Notes in Mathematics, Vol. 340}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1973}, pages = {x+438}, mrclass = {14-06}, mrnumber = {50 \#7135} } @Article{ shafarevich:exp, author = {Shafarevich, I.\thinspace{}R.}, title = {Exponents of elliptic curves}, journal = {Dokl. Akad. Nauk SSSR (N.S.)}, volume = {114}, year = {1957}, pages = {714--716} } @Article{ shimizu:zeta, author = {Shimizu, H.}, title = {On zeta functions of quaternion algebras}, journal = {Ann. of Math. (2)}, volume = {81}, year = {1965}, pages = {166--193} } @Article{ shimura:factors, author = {Shimura, G.}, title = {On the factors of the jacobian variety of a modular function field}, journal = {J. Math. Soc. Japan}, volume = {25}, number = {3}, year = {1973}, pages = {523--544} } @Book{ shimura:intro, author = {Shimura, G.}, title = {Introduction to the arithmetic theory of automorphic functions}, note = {Reprint of the 1971 original, Kan Memorial Lectures, 1}, publisher = {Princeton University Press}, address = {Princeton, NJ}, year = {1994}, pages = {xiv+271}, isbn = {0-691-08092-5} } @Article{ shimura:onperiods, author = {Shimura, G.}, title = {On the periods of modular forms}, journal = {Math. Ann.}, volume = {229}, pages = {211--221}, year = {1977} } @Article{ shimura:reciprocity, author = {Shimura, G.}, title = {A reciprocity law in non-solvable extensions}, journal = {J. Reine Angew. Math.}, volume = {221}, year = {1966}, pages = {209--220} } @Article{ shimura:surles, author = {Shimura, G.}, title = {Sur les \protect{int\'egrales} \protect{attach\'ees} aux formes automorphes}, journal = {J. Math. Soc. Japan}, volume = {11}, year = {1959}, pages = {291--311} } @Book{ silverman-tate, author = {Silverman, J.\thinspace{}H. and Tate, J.}, title = {Rational points on elliptic curves}, series = {Undergraduate Texts in Mathematics}, publisher = {Springer-Verlag}, address = {New York}, year = {1992}, pages = {x+281}, isbn = {0-387-97825-9}, mrclass = {11-01 (11D25 11G05 14H52)}, mrnumber = {93g:11003}, mrreviewer = {Andrew Bremner} } @Book{ silverman:aec, author = {Silverman, J.\thinspace{}H.}, title = {The arithmetic of elliptic curves}, note = {Corrected reprint of the 1986 original}, publisher = {Springer-Verlag}, address = {New York}, year = {1992}, pages = {xii+400}, isbn = {0-387-96203-4} } @Book{ silverman:aec2, author = {Silverman, J.\thinspace{}H.}, title = {Advanced topics in the arithmetic of elliptic curves}, publisher = {Springer-Verlag}, address = {New York}, year = {1994}, pages = {xiv+525}, isbn = {0-387-94328-5} } @Article{ siman_wong:lots_of_sha, author = {Wong, Siman}, title = {Elliptic curves and class number divisibility}, journal = {Internat. Math. Res. Notices}, fjournal = {International Mathematics Research Notices}, year = {1999}, number = {12}, pages = {661--672}, issn = {1073-7928}, mrclass = {11G05 (11R29)}, mrnumber = {2000i:11088}, mrreviewer = {Kenneth Kramer} } @Article{ skinner-wiles:ordinary, author = {Skinner, C.\thinspace{}M. and Wiles, A.\thinspace{}J.}, title = {Ordinary representations and modular forms}, journal = {Proc. Nat. Acad. Sci. U.S.A.}, fjournal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {94}, year = {1997}, number = {20}, pages = {10520--10527}, issn = {0027-8424}, coden = {PNASA6} } @Book{ slnm601, title = {Modular functions of one variable. \protect{V}}, booktitle = {Proceedings of the Second International Conference, held at the University of Bonn, Bonn, July 2--14, 1976}, note = {Edited by J-P. Serre and D. B. Zagier, Lecture Notes in Mathematics, Vol. 601}, publisher = {Springer-Verlag}, address = {Berlin}, year = {1977}, pages = {i+294} } @Article{ sokurov:modsym, author = {{\v{S}}okurov, V. V.}, title = {Modular symbols of arbitrary weight}, journal = {Funkcional. Anal. i Prilo\v zen.}, volume = {10}, year = {1976}, number = {1}, pages = {95--96}, mrclass = {10D05}, mrnumber = {55 #269}, mrrevr = {K.-B. Gundlach} } @Article{ stein-verrill:periods, author = "Stein, W.\thinspace{}A. and Verrill, H.\thinspace{}A.", title = {Computing period lattices associated to newforms}, journal = {In preparation}, year = {2000} } @Article{ stein-verrill:transportable, author = "Stein, W.\thinspace{}A. and Verrill, H.\thinspace{}A.", title = {Cuspidal modular symbols are transportable}, journal = {LMS J. Comput. Math.}, fjournal = {LMS Journal of Computation and Mathematics}, volume = {4}, year = {2001}, pages = {170--181 (electronic)}, issn = {1461-1570}, mrclass = {11F67}, mrnumber = {1 901 355} } @incollection {stein-watkins:ants5, AUTHOR = {Stein, W. and Watkins, M.}, TITLE = {A database of elliptic curves---first report}, BOOKTITLE = {Algorithmic number theory (Sydney, 2002)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {2369}, PAGES = {267--275}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2002}, MRCLASS = {11G05 (11Y35)}, MRNUMBER = {MR2041090 (2005h:11113)}, } @proceedings {MR2041068, TITLE = {Algorithmic number theory}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {2369}, BOOKTITLE = {Proceedings of the 5th International Symposium (ANTS-V) held at the University of Sydney, Sydney, July 7--12, 2002}, EDITOR = {Fieker, Claus and Kohel, David R.}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2002}, PAGES = {x+517}, ISBN = {3-540-43863-7}, MRCLASS = {11-06}, MRNUMBER = {MR2041068 (2004j:11002)}, } @Article{ stein:bsdmagma, author = {Stein, W.}, title = {Studying the {B}irch and {S}winnerton-{D}yer {C}onjecture for {M}odular {A}belian {V}arieties {U}sing {MAGMA}}, journal = {to appear in J.~Cannon, ed., {\em Computational Experiments in Algebra and Geometry}, Springer-Verlag}, year = {2004} } @Article{ stein:congruence, author = "Stein, W.\thinspace{}A.", title = {Congruences between modular forms}, journal = {Notes}, year = {1999} } @Article{ stein:database, author = "Stein, W.\thinspace{}A.", title = {The modular forms database,\hfill\\ \protect{\tt http://modular.math.washington.edu}} } @Article{ stein:hecke, author = "Stein, W.\thinspace{}A.", title = {\protect{{\tt HECKE}: The} modular symbols calculator}, journal = {Software (available online)}, year = {1999} } @Article{ stein:index, author = {Stein, W.\thinspace{}A.}, title = {There are genus one curves over {$\mathbf{Q}$} of every odd index}, journal = {J. Reine Angew. Math.}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, volume = {547}, year = {2002}, pages = {139--147}, issn = {0075-4102}, coden = {JRMAA8}, mrclass = {11G05 (11G18)}, mrnumber = {2003c:11059}, mrreviewer = {Imin Chen} } @Article{ stein:modsyms, author = "Stein, W.\thinspace{}A.", title = {An introduction to computing modular forms using modular symbols}, journal = {to appear in an MSRI Proceedings} } @Article{ stein:nonsquaresha, author = {Stein, W.\thinspace{}A.}, title = {Shafarevich-{T}ate {G}roups of {N}onsquare {O}rder}, publisher = {Birkh\"auser}, journal = {Modular Curves and Abelian Varieties, Progress of Mathematics}, year = {2004}, pages = {277--289} } @Article{ stein:phd, author = "Stein, W.\thinspace{}A.", title = {Explicit approaches to modular abelian varieties}, journal = {Ph.D. thesis, University of California, Berkeley}, year = {2000} } @Article{ stein:vismordell, author = {Stein, W.\thinspace{}A.}, title = {{V}isualizing {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves {U}sing {S}hafarevich-{T}ate {G}roups}, year = {2002}, journal = {In preparation} } @Article{ stevens:param, author = {Stevens, G.}, title = {Stickelberger elements and modular parametrizations of elliptic curves}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {98}, year = {1989}, number = {1}, pages = {75--106}, issn = {0020-9910}, coden = {INVMBH}, mrclass = {11G05 (11F11)}, mrnumber = {90m:11089}, mrreviewer = {Sheldon Kamienny} } @Book{ stevens:thesis, author = {Stevens, G.}, title = {Arithmetic on modular curves}, publisher = {Birkh\"auser Boston Inc.}, address = {Boston, Mass.}, year = {1982}, pages = {xvii+214}, isbn = {3-7643-3088-0}, mrclass = {11G40 (11F67 11G30 14G10 14G13)}, mrnumber = {87b:11050}, mrrevr = {Ernst Kani} } @InCollection{ sturm:cong, author = {Sturm, J.}, title = {On the congruence of modular forms}, booktitle = {Number theory (New York, 1984--1985)}, pages = {275--280}, publisher = {Springer}, address = {Berlin}, year = {1987} } @Book{ swinnerton-dyer:abvars, author = {Swinnerton-Dyer, H. P. F.}, title = {Analytic theory of abelian varieties}, note = {London Mathematical Society Lecture Note Series, No. 14}, publisher = {Cambridge University Press}, address = {London}, year = {1974}, pages = {viii+90}, mrclass = {14K20}, mrnumber = {51 \#3180}, mrreviewer = {H. Klingen} } @InCollection{ tate:antwerpiv, author = {Tate, J.}, title = {Algorithm for determining the type of a singular fiber in an elliptic pencil}, booktitle = {Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, pages = {33--52. Lecture Notes in Math., Vol. 476}, publisher = {Springer}, address = {Berlin}, year = {1975}, mrclass = {14G25 (14K15)}, mrnumber = {52 \#13850}, mrreviewer = {J. S. Milne} } @InCollection{ tate:bsd, author = {Tate, J.}, title = {On the conjectures of {B}irch and {S}winnerton-{D}yer and a geometric analog}, booktitle = {S\'eminaire Bourbaki, Vol.\ 9}, pages = {Exp.\ No.\ 306, 415--440}, publisher = {Soc. Math. France}, address = {Paris}, year = {1965/66} } @InCollection{ tate:duality, author = {Tate, J.}, title = {Duality theorems in {G}alois cohomology over number fields}, booktitle = {Proc. Internat. Congr. Mathematicians (Stockholm, 1962)}, pages = {288--295}, publisher = {Inst. Mittag-Leffler}, address = {Djursholm}, year = {1963}, mrclass = {10.66}, mrnumber = {31 \#168} } @InCollection{ tate:global, author = {Tate, J.\thinspace{}T.}, title = {Global class field theory}, booktitle = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, pages = {162--203}, publisher = {Thompson, Washington, D.C.}, year = {1967} } @Article{ tate:nonexistence, author = {Tate, J.\thinspace{}T.}, title = {The non-existence of certain \protect{Galois} extensions of \protect{$\mathbf{Q}$} unramified outside \protect{$2$}}, journal = {Contemporary Math.}, volume = {174}, year = {1994}, pages = {153--156} } @Article{ taylor-wiles:fermat, author = {Taylor, R. and Wiles, A.\thinspace{}J.}, title = {Ring-theoretic properties of certain \protect{H}ecke algebras}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {141}, year = {1995}, number = {3}, pages = {553--572}, issn = {0003-486X}, coden = {ANMAAH} } @Article{ tunnell:artin, author = {Tunnell, J.}, title = {Artin's conjecture for representations of octahedral type}, journal = {Bull. Amer. Math. Soc. (N.S.)}, fjournal = {American Mathematical Society. Bulletin. 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