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Author: William A. Stein
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@article {rubin-silverberg:ranks,
3
AUTHOR = {Rubin, Karl and Silverberg, Alice},
4
TITLE = {Ranks of elliptic curves},
5
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
6
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
7
VOLUME = {39},
8
YEAR = {2002},
9
NUMBER = {4},
10
PAGES = {455--474 (electronic)},
11
ISSN = {0273-0979},
12
CODEN = {BAMOAD},
13
MRCLASS = {11G05 (11G40)},
14
MRNUMBER = {MR1920278 (2003f:11080)},
15
MRREVIEWER = {Ioannis Papadopoulos},
16
}
17
18
19
@incollection {silverberg:open_questions,
20
AUTHOR = {Silverberg, Alice},
21
TITLE = {Open questions in arithmetic algebraic geometry},
22
BOOKTITLE = {Arithmetic algebraic geometry (Park City, UT, 1999)},
23
SERIES = {IAS/Park City Math. Ser.},
24
VOLUME = {9},
25
PAGES = {83--142},
26
PUBLISHER = {Amer. Math. Soc.},
27
ADDRESS = {Providence, RI},
28
YEAR = {2001},
29
MRCLASS = {11Gxx (14Gxx)},
30
MRNUMBER = {MR1860041 (2002g:11073)},
31
MRREVIEWER = {Joseph H. Silverman},
32
}
33
34
@book {MR1860012,
35
TITLE = {Arithmetic algebraic geometry},
36
SERIES = {IAS/Park City Mathematics Series},
37
VOLUME = {9},
38
EDITOR = {Conrad, Brian and Rubin, Karl},
39
NOTE = {Including papers from the Graduate Summer School of the
40
Institute for Advanced Study/Park City Mathematics Institute
41
held in Park City, UT, June 20--July 10, 1999},
42
PUBLISHER = {American Mathematical Society},
43
ADDRESS = {Providence, RI},
44
YEAR = {2001},
45
PAGES = {xiv+569},
46
ISBN = {0-8218-2173-3},
47
MRCLASS = {11-06 (14-06)},
48
MRNUMBER = {MR1860012 (2002d:11003)},
49
}
50
51
52
@incollection {goldfeld:conjectures_quadratic,
53
AUTHOR = {Goldfeld, Dorian},
54
TITLE = {Conjectures on elliptic curves over quadratic fields},
55
BOOKTITLE = {Number theory, Carbondale 1979 (Proc. Southern Illinois Conf.,
56
Southern Illinois Univ., Carbondale, Ill., 1979)},
57
SERIES = {Lecture Notes in Math.},
58
VOLUME = {751},
59
PAGES = {108--118},
60
PUBLISHER = {Springer},
61
ADDRESS = {Berlin},
62
YEAR = {1979},
63
MRCLASS = {12A70 (14K07)},
64
MRNUMBER = {MR564926 (81i:12014)},
65
MRREVIEWER = {Kenneth Kramer},
66
}
67
68
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@proceedings {MR564918,
70
TITLE = {Number theory, {C}arbondale 1979},
71
SERIES = {Lecture Notes in Mathematics},
72
VOLUME = {751},
73
BOOKTITLE = {Proceedings of the Southern Illinois Number Theory Conference,
74
held at Southern Illinois University, Carbondale, Ill., March
75
30--31, 1979},
76
EDITOR = {Nathanson, Melvyn B.},
77
PUBLISHER = {Springer},
78
ADDRESS = {Berlin},
79
YEAR = {1979},
80
PAGES = {iv+342},
81
ISBN = {3-540-09559-4},
82
MRCLASS = {10-06},
83
MRNUMBER = {MR564918 (81a:10004)},
84
}
85
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87
@article {kramarz-zagier,
88
AUTHOR = {Zagier, D. and Kramarz, G.},
89
TITLE = {Numerical investigations related to the {$L$}-series of
90
certain elliptic curves},
91
JOURNAL = {J. Indian Math. Soc. (N.S.)},
92
FJOURNAL = {The Journal of the Indian Mathematical Society. New Series},
93
VOLUME = {52},
94
YEAR = {1987},
95
PAGES = {51--69 (1988)},
96
ISSN = {0019-5839},
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CODEN = {JIMTA2},
98
MRCLASS = {11G05 (11G40 11Y50)},
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MRNUMBER = {MR989230 (90d:11072)},
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MRREVIEWER = {M. Ram Murty},
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}
102
103
@article{darmon-pollack,
104
author = {Darmon, H. and Pollack, R.},
105
title = {The efficient calculation of {S}tark-{H}eegner points
106
via overconvergent modular symbols},
107
year = {2004}
108
}
109
110
@article{kraus,
111
author = {Kraus, Alain},
112
title = {D\'etermination du poids et du conducteur associ\'es
113
aux repr\'esentations des points de $p$-torsion d'une courbe elliptique}
114
}
115
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@article{math252,
117
author = {Stein, William},
118
title = {Modular Abelian Varieties, \hfill\mbox{}
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{\tt http://modular.fas.harvard.edu/edu/Fall2003/252/}},
120
year = {2003}
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}
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@article{dembele,
124
author = {Dembele, Lassina},
125
title = {Quaternionic Modular Symbols and Computing {H}ilbert Modular Forms,
126
\hfill\mbox{}
127
{\tt http://modular.fas.harvard.edu/mcs/archive/Spring2004/dembele.html}},
128
year = {2004}
129
}
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@article{lemelin:dominic,
132
author = {Lemelin, Dominic},
133
title = {Mazur-Tate Type Conjectures for Elliptic Curves Defined over Quadratic Imaginary Fields},
134
year = {2001}
135
}
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@article{diderot:thesis,
138
author = {Diderot, Denis},
139
title = {P\'eriodes de formes modulaires de poids 1},
140
year = {2001},
141
journal = {{\tt http://modular.fas.harvard.edu/scans/papers/diderot/}}
142
}
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@article{basmaji:thesis,
146
author = {Basmaji, Jacques},
147
TITLE = {Ein Algorithmus zur Berechnung von Hecke-Operatoren und
148
Anwendungen auf modulare Kurven},
149
YEAR = {1996},
150
journal={{\tt http://modular.fas.harvard.edu/scans/papers/basmaji/}}
151
}
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@article {sokurov:shimura,
154
AUTHOR = {{\v{S}}okurov, V.\thinspace{}V.},
155
TITLE = {Shimura integrals of cusp forms},
156
JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
157
FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
158
VOLUME = {44},
159
YEAR = {1980},
160
NUMBER = {3},
161
PAGES = {670--718, 720},
162
ISSN = {0373-2436},
163
MRCLASS = {10D12 (14K22)},
164
MRNUMBER = {MR582162 (82b:10029)},
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MRREVIEWER = {K.-B. Gundlach},
166
}
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@book {knuth2,
169
AUTHOR = {Knuth, Donald E.},
170
TITLE = {The art of computer programming. {V}ol. 2},
171
EDITION = {Third},
172
NOTE = {Seminumerical algorithms,
173
Addison-Wesley Series in Computer Science and Information
174
Processing},
175
PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.}
176
}
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@Article{ csirik-wetherell-zieve:g0,
179
author = {Csirik, Janos A. and Wetherell, Joseph L. and Zieve,
180
Michael E.},
181
title = {On the genera of {$X_0(N)$}},
182
journal = {See {\tt http://www.csirik.net/papers.html}},
183
year = {2001}
184
}
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@Article{ pr:exp,
187
author = {Perrin-Riou, Bernadette},
188
title = {Arithm\'etique des courbes elliptiques \`a r\'eduction
189
supersinguli\`ere en {$p$}},
190
journal = {Experiment. Math.},
191
fjournal = {Experimental Mathematics},
192
volume = {12},
193
year = {2003},
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number = {2},
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pages = {155--186},
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issn = {1058-6458},
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mrclass = {11G05},
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mrnumber = {MR2016704}
199
}
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@Article{ mtt,
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author = {Mazur, B. and Tate, J. and Teitelbaum, J.},
203
title = {On {$p$}-adic analogues of the conjectures of {B}irch and
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{S}winnerton-{D}yer},
205
journal = {Invent. Math.},
206
fjournal = {Inventiones Mathematicae},
207
volume = {84},
208
year = {1986},
209
number = {1},
210
pages = {1--48},
211
issn = {0020-9910},
212
coden = {INVMBH},
213
mrclass = {11G40 (11G05 14G10)},
214
mrnumber = {MR830037 (87e:11076)},
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mrreviewer = {Kenneth A. Ribet}
216
}
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@Article{ serre:asymptotique,
219
author = {Serre, Jean-Pierre},
220
title = {R\'epartition asymptotique des valeurs propres de
221
l'op\'erateur de {H}ecke {$T\sb p$}},
222
journal = {J. Amer. Math. Soc.},
223
fjournal = {Journal of the American Mathematical Society},
224
volume = {10},
225
year = {1997},
226
number = {1},
227
pages = {75--102},
228
issn = {0894-0347},
229
mrclass = {11F30 (11F25 11G20 11N37 11R45)},
230
mrnumber = {97h:11048},
231
mrreviewer = {Glenn Stevens}
232
}
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@Book{ iwaniec:topics,
235
author = {Iwaniec, Henryk},
236
title = {Topics in classical automorphic forms},
237
series = {Graduate Studies in Mathematics},
238
volume = {17},
239
publisher = {American Mathematical Society},
240
address = {Providence, RI},
241
year = {1997},
242
pages = {xii+259},
243
isbn = {0-8218-0777-3},
244
mrclass = {11Fxx (11-02)},
245
mrnumber = {98e:11051},
246
mrreviewer = {B. Ramakrishnan}
247
}
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249
@Article{ gordon:dlp,
250
author = {Gordon, D.},
251
date = {2004},
252
title = {Discrete Logarithm Problem, \hfill\\ {\tt
253
http://www.win.tue.nl/\~{ }henkvt/Content.html}}
254
}
255
256
@Proceedings{ mr98i:94002,
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title = {Advances in cryptology---{EUROCRYPT} '97},
258
series = {Lecture Notes in Computer Science},
259
volume = {1233},
260
booktitle = {Proceedings of the 16th International Conference on the
261
Theory and Application of Cryptographic Techniques held in
262
Konstanz, May 11--15, 1997},
263
editor = {Fumy, Walter},
264
publisher = {Springer-Verlag},
265
address = {Berlin},
266
year = {1997},
267
pages = {xii+509},
268
isbn = {3-540-62975-0},
269
mrclass = {94-06 (68P25 94A60)},
270
mrnumber = {98i:94002}
271
}
272
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@Article{ nechaev:lower,
274
author = {Nechaev, V. I.},
275
title = {On the complexity of a deterministic algorithm for a
276
discrete logarithm},
277
journal = {Mat. Zametki},
278
fjournal = {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki},
279
volume = {55},
280
year = {1994},
281
number = {2},
282
pages = {91--101, 189},
283
issn = {0025-567X},
284
mrclass = {11Y16},
285
mrnumber = {96a:11145}
286
}
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@InCollection{ shoup:lower,
289
author = {Shoup, Victor},
290
title = {Lower bounds for discrete logarithms and related
291
problems},
292
booktitle = {Advances in cryptology---EUROCRYPT '97 (Konstanz)},
293
series = {Lecture Notes in Comput. Sci.},
294
volume = {1233},
295
pages = {256--266},
296
publisher = {Springer},
297
address = {Berlin},
298
year = {1997},
299
mrclass = {94A60 (68P25 68Q25)},
300
mrnumber = {98j:94023}
301
}
302
303
@Article{ gordon:dlog,
304
author = {Gordon, Daniel M.},
305
title = {Discrete logarithms in {${\rm GF}(p)$} using the number
306
field sieve},
307
journal = {SIAM J. Discrete Math.},
308
fjournal = {SIAM Journal on Discrete Mathematics},
309
volume = {6},
310
year = {1993},
311
number = {1},
312
pages = {124--138},
313
issn = {0895-4801},
314
coden = {SJDMEC},
315
mrclass = {11Y16 (11N36)},
316
mrnumber = {94d:11104},
317
mrreviewer = {Joe P. Buhler}
318
}
319
320
@Article{ python,
321
author = {Rossum, Guido van},
322
title = {Python,\newline{\tt http://www.python.org}}
323
}
324
325
@Article{ cha:shabound,
326
author = {Cha, Byungchul},
327
title = {Vanishing of {S}ome {C}ohomology {G}roups and {B}ounds for
328
the {S}hafarevich-{T}ate {G}roups of {E}lliptic {C}urves},
329
journal = {Johns-Hopkins Ph.D. Thesis},
330
year = {2003}
331
}
332
333
@Article{ cassels:7,
334
author = {Cassels, J. W. S.},
335
title = {Arithmetic on curves of genus 1. {VIII}. {O}n conjectures
336
of {B}irch and {S}winnerton-{D}yer},
337
journal = {J. Reine Angew. Math.},
338
volume = {217},
339
year = {1965},
340
pages = {180--199},
341
mrclass = {14.48 (14.49)},
342
mrnumber = {31 \#3420},
343
mrreviewer = {T. Ono}
344
}
345
346
@Article{ kedlaya:mw1,
347
author = {Kedlaya, K.\thinspace{}S.},
348
title = {Errata for: ``{C}ounting points on hyperelliptic curves
349
using {M}onsky-{W}ashnitzer cohomology'' [{J}. {R}amanujan
350
{M}ath.\ {S}oc.\ {\bf 16} (2001), no. 4, 323--338},
351
note = {Dedicated to Professor K. S. Padmanabhan},
352
journal = {J. Ramanujan Math. Soc.},
353
fjournal = {Journal of the Ramanujan Mathematical Society},
354
volume = {18},
355
year = {2003},
356
number = {4},
357
pages = {417--418},
358
issn = {0970-1249},
359
mrclass = {14G05 (11G25 14F43 14G15)},
360
mrnumber = {2 043 934}
361
}
362
363
@Article{ abbott:padic,
364
author = {Abbott, J.},
365
title = {Recovery of algebraic numbers from their $p$-adic
366
approximations},
367
journal = {Proceedings of the ACM-SIGSAM 1989 international symposium
368
on Symbolic and algebraic computation},
369
pages = {112--120},
370
year = {1989},
371
isbn = {0-89791-325-6},
372
publisher = {ACM Press, New York, NY, USA}
373
}
374
375
@Article{ tate:arithmetic,
376
author = {Tate, J.},
377
title = {The arithmetic of elliptic curves},
378
journal = {Invent. Math.},
379
volume = {23},
380
year = {1974},
381
pages = {179--206},
382
mrclass = {10D05 (14G25 14K15)},
383
mrnumber = {54 \#7380},
384
mrreviewer = {A. P. Ogg}
385
}
386
387
@Article{ mazur-tate:sigma,
388
author = {Mazur, B. and Tate, J.},
389
title = {The {$p$}-adic sigma function},
390
journal = {Duke Math. J.},
391
fjournal = {Duke Mathematical Journal},
392
volume = {62},
393
year = {1991},
394
number = {3},
395
pages = {663--688},
396
issn = {0012-7094},
397
coden = {DUMJAO},
398
mrclass = {11G07 (11S80)},
399
mrnumber = {93d:11059}
400
}
401
402
@Book{ artin-tate:cft,
403
author = {Artin, E. and Tate, J.},
404
title = {Class field theory},
405
series = {Advanced Book Classics},
406
edition = {Second},
407
publisher = {Addison-Wesley Publishing Company Advanced Book Program},
408
address = {Redwood City, CA},
409
year = {1990},
410
pages = {xxxviii+259},
411
isbn = {0-201-51011-1},
412
mrclass = {11R37 (11-01 11R34)},
413
mrnumber = {91b:11129}
414
}
415
416
@Article{ mahler:inequalities,
417
author = {Mahler, K.},
418
title = {Inequalities for ideal bases in algebraic number fields},
419
journal = {J. Austral. Math. Soc.},
420
volume = {4},
421
year = {1964},
422
pages = {425--448},
423
mrclass = {12.50},
424
mrnumber = {31 \#1243},
425
mrreviewer = {L. R. McCulloh}
426
}
427
428
@Article{ iwasawa:adele,
429
author = {Iwasawa, K.},
430
title = {On the rings of valuation vectors},
431
journal = {Ann. of Math. (2)},
432
volume = {57},
433
year = {1953},
434
pages = {331--356},
435
mrclass = {10.0X},
436
mrnumber = {14,849a},
437
mrreviewer = {J. T. Tate}
438
}
439
440
@Book{ lang:algebraic_numbers,
441
author = {Lang, S.},
442
title = {Algebraic numbers},
443
publisher = {Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo
444
Alto-London},
445
year = {1964},
446
pages = {ix+163},
447
mrclass = {10.65},
448
mrnumber = {28 \#3974},
449
mrreviewer = {S. Chowla}
450
}
451
452
@Book{ cassels:lectures,
453
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
454
title = {Lectures on elliptic curves},
455
series = {London Mathematical Society Student Texts},
456
volume = {24},
457
publisher = {Cambridge University Press},
458
address = {Cambridge},
459
year = {1991},
460
pages = {vi+137},
461
isbn = {0-521-41517-9; 0-521-42530-1},
462
mrclass = {11G05 (14H52)},
463
mrnumber = {92k:11058},
464
mrreviewer = {Philippe Satg{\'e}}
465
}
466
467
@Article{ lenstra:pell,
468
author = {Lenstra, Jr., H.\thinspace{}W.},
469
title = {Solving the {P}ell equation},
470
journal = {Notices Amer. Math. Soc.},
471
fjournal = {Notices of the American Mathematical Society},
472
volume = {49},
473
year = {2002},
474
number = {2},
475
pages = {182--192},
476
issn = {0002-9920},
477
coden = {AMNOAN},
478
mrclass = {11D09 (01A99 11R27)},
479
mrnumber = {2002i:11028},
480
mrreviewer = {Duncan A. Buell}
481
}
482
483
@Book{ artin:algebra,
484
author = {Artin, M.},
485
title = {Algebra},
486
publisher = {Prentice Hall Inc.},
487
address = {Englewood Cliffs, NJ},
488
year = {1991},
489
pages = {xviii+618},
490
isbn = {0-13-004763-5},
491
mrclass = {00A05 (11-01 12-01 13-01 15-01 16-01 20-01)},
492
mrnumber = {92g:00001},
493
mrreviewer = {Gerald J. Janusz}
494
}
495
496
@Book{ artin:ant,
497
author = {Artin, E.},
498
title = {Theory of algebraic numbers},
499
series = {Notes by Gerhard W\"urges from lectures held at the
500
Mathematisches Institut, G\"ottingen, Germany, in the
501
Winter Semester},
502
volume = {1956/7},
503
publisher = {George Striker, Schildweg 12, G\"ottingen},
504
year = {1959},
505
pages = {172},
506
mrclass = {10.65},
507
mrnumber = {24 \#A1884},
508
mrreviewer = {L. Carlitz}
509
}
510
511
@Book{ am,
512
author = {Atiyah, M. F. and Macdonald, I. G.},
513
title = {Introduction to commutative algebra},
514
publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
515
Mills, Ont.},
516
year = {1969},
517
pages = {ix+128},
518
mrclass = {13.00},
519
mrnumber = {39 \#4129},
520
mrreviewer = {J. A. Johnson}
521
}
522
523
@Article{ agashe,
524
author = {Agashe, A.},
525
title = {On invisible elements of the {T}ate-{S}hafarevich group},
526
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
527
fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
528
Math\'ematique},
529
volume = {328},
530
year = {1999},
531
number = {5},
532
pages = {369--374},
533
issn = {0764-4442},
534
coden = {CASMEI},
535
mrclass = {11Gxx},
536
mrnumber = {1 678 131}
537
}
538
539
@Article{ agashe-stein:bsd,
540
author = "Agashe, A. and Stein, W.\thinspace{}A.",
541
title = "Visible {E}vidence for the {B}irch and {S}winnerton-{D}yer
542
{C}onjecture for {M}odular {A}belian {V}arieties of
543
{A}nalytic {R}ank~$0$",
544
date = 2004,
545
journal = {to appear in Math. of Computation}
546
}
547
548
@Article{ agashe-stein:manin,
549
author = "Agashe, A. and Stein, W.\thinspace{}A.",
550
title = "The Manin Constant, Congruence Primes, and the Modular
551
Degree",
552
year = {2004},
553
journal = {Preprint,\hfill\\ {\tt
554
http://modular.fas.harvard.edu/papers/manin-agashe/}}
555
}
556
557
@Article{ agashe-stein:schoof-appendix,
558
author = {Lario, J.-C. and Schoof, R.}
559
}
560
561
@Article{ agashe-stein:visibility,
562
author = {Agashe, A. and Stein, W.\thinspace{}A.},
563
title = {Visibility of {S}hafarevich-{T}ate groups of abelian
564
varieties},
565
journal = {J. Number Theory},
566
fjournal = {Journal of Number Theory},
567
volume = {97},
568
year = {2002},
569
number = {1},
570
pages = {171--185},
571
issn = {0022-314X},
572
coden = {JNUTA9},
573
mrclass = {11G40 (11G10 14K15)},
574
mrnumber = {2003h:11070},
575
mrreviewer = {Chandan Singh Dalawat}
576
}
577
578
@Article{ agashe:invisible,
579
author = {Agash{\'e}, Amod},
580
title = {On invisible elements of the {T}ate-{S}hafarevich group},
581
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
582
fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
583
Math\'ematique},
584
volume = {328},
585
year = {1999},
586
number = {5},
587
pages = {369--374},
588
issn = {0764-4442},
589
coden = {CASMEI},
590
mrclass = {11G40 (11G10 11G18)},
591
mrnumber = {2000e:11083},
592
mrreviewer = {Kenneth Kramer}
593
}
594
595
@Article{ agashe:phd,
596
author = "Agashe, A.",
597
title = {The {B}irch and {S}winnerton-{D}yer formula for modular
598
abelian varieties of analytic rank~$0$},
599
journal = {Ph.D. thesis, University of California, Berkeley},
600
year = {2000}
601
}
602
603
@Book{ antwerpiv,
604
title = {Modular functions of one variable. {I}{V}},
605
booktitle = {Proceedings of the International Summer School on Modular
606
Functions of One Variable and Arithmetical Applications,
607
RUCA, University of Antwerp, Antwerp, July 17--August 3,
608
1972},
609
editor = {Birch, B.\thinspace{}J. and Kuyk, W.},
610
note = {Lecture Notes in Mathematics, Vol. 476},
611
publisher = {Springer-Verlag},
612
address = {Berlin},
613
year = {1975},
614
pages = {iv+151}
615
}
616
617
@Article{ artin:conjecture,
618
author = {Artin, E.},
619
title = {{\"U}ber eine neue {A}rt von {L}-Reihen},
620
journal = {Abh. Math. Sem. Univ. Hamburg},
621
volume = {3},
622
year = {1923 or 1924??? CHECK!},
623
pages = {89--108}
624
}
625
626
@Article{ artin:conjecture2,
627
author = {Artin, E},
628
title = {Zur {T}heorie der {L}-{R}eihen mit allgemeinen
629
{G}ruppencharakteren},
630
journal = {Abh. math. Semin. Univ. Hamburg},
631
volume = {8},
632
year = {1930},
633
pages = {292--306}
634
}
635
636
@Article{ ash-stevens,
637
author = {Ash, A. and Stevens, G.},
638
title = {Cohomology of arithmetic groups and congruences between
639
systems of {H}ecke eigenvalues},
640
journal = {J. Reine Angew. Math.},
641
fjournal = {Journal f\"ur die Reine und Angewandte Mathematik},
642
volume = {365},
643
year = {1986},
644
pages = {192--220},
645
issn = {0075-4102},
646
coden = {JRMAA8}
647
}
648
649
@Article{ atkin-lehner,
650
author = {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.},
651
title = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
652
journal = {Math. Ann.},
653
volume = {185},
654
year = {1970},
655
pages = {134--160}
656
}
657
658
@Article{ bdsbt,
659
author = {Buzzard, K. and Dickinson, M. and Shepherd-Barron, N. and
660
Taylor, R.},
661
title = {On icosahedral {A}rtin representations},
662
journal = { \protect{\tt
663
http://www.math.harvard.edu/HTML/Individuals/Richard\_Taylor.html}}
664
,
665
date = {2000}
666
}
667
668
@Book{ bgr,
669
author = {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.},
670
title = {Non-{A}rchimedean analysis: A systematic approach to rigid
671
analytic geometry},
672
publisher = {Springer-Verlag},
673
address = {Berlin},
674
year = {1984},
675
pages = {xii+436},
676
isbn = {3-540-12546-9},
677
mrclass = {32K10 (30G05 46P05)},
678
mrnumber = {86b:32031},
679
mrrevr = {W. Bartenwerfer}
680
}
681
682
@InCollection{ birch:atkin,
683
author = {Birch, B.},
684
title = {Atkin and the {A}tlas {L}ab},
685
booktitle = {Proceedings of the conference in honor of
686
A.\thinspace{}O.\thinspace{}L. Atkin held at the University
687
of Illinois, Chicago, IL, September 1995},
688
pages = {13--20},
689
publisher = {Amer. Math. Soc.},
690
address = {Providence, RI},
691
year = {1998},
692
mrclass = {11-03 (01A60 11F30 11F33)},
693
mrnumber = {99c:11002},
694
mrrevr = {V. Kumar Murty}
695
}
696
697
@InCollection{ birch:bsd,
698
author = {Birch, B.\thinspace{}J.},
699
title = {Elliptic curves over \protect{${\mathbf{Q}}$: {A}}
700
progress report},
701
booktitle = {1969 Number Theory Institute (Proc. Sympos. Pure Math.,
702
Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969)},
703
pages = {396--400},
704
publisher = {Amer. Math. Soc.},
705
address = {Providence, R.I.},
706
year = {1971}
707
}
708
709
@InCollection{ birch:cyclo,
710
author = {Birch, B.\thinspace{}J.},
711
title = {Cyclotomic fields and {K}ummer extensions},
712
booktitle = {Algebraic Number Theory (Proc. Instructional Conf.,
713
Brighton, 1965)},
714
pages = {85--93},
715
publisher = {Thompson, Washington, D.C.},
716
year = {1967}
717
}
718
719
@InCollection{ birch:edsac,
720
author = {Birch, B. J.},
721
title = {Conjectures concerning elliptic curves},
722
booktitle = {Proceedings of Symposia in Pure Mathematics, VIII},
723
pages = {106--112},
724
publisher = {Amer. Math. Soc.},
725
address = {Providence, R.I.},
726
year = {1965},
727
mrclass = {14.49 (14.40)},
728
mrnumber = {30 \#4759},
729
mrreviewer = {J. W. S. Cassels}
730
}
731
732
@InCollection{ birch:hecke_actions,
733
author = {Birch, B. J.},
734
title = {Hecke actions on classes of ternary quadratic forms},
735
booktitle = {Computational number theory (Debrecen, 1989)},
736
pages = {191--212},
737
publisher = {de Gruyter},
738
address = {Berlin},
739
year = {1991},
740
mrclass = {11E45 (11E20 11F11 11G05 11Y35)},
741
mrnumber = {93i:11047},
742
mrrevr = {Rainer Schulze-Pillot}
743
}
744
745
@InCollection{ bloch-kato,
746
author = {Bloch, S. and Kato, K.},
747
title = {\protect{${L}$}-functions and \protect{T}amagawa numbers
748
of motives},
749
booktitle = {The Grothendieck Festschrift, Vol. \protect{I}},
750
pages = {333--400},
751
publisher = {Birkh\"auser Boston},
752
address = {Boston, MA},
753
year = {1990}
754
}
755
756
@Article{ bockle:density,
757
author = {B{\"o}ckle, Gebhard},
758
title = {On the density of modular points in universal deformation
759
spaces},
760
journal = {Amer. J. Math.},
761
fjournal = {American Journal of Mathematics},
762
volume = {123},
763
year = {2001},
764
number = {5},
765
pages = {985--1007},
766
issn = {0002-9327},
767
coden = {AJMAAN},
768
mrclass = {11F80},
769
mrnumber = {1 854 117}
770
}
771
772
@Article{ bolling:sha,
773
author = {B{\"o}lling, Reinhard},
774
title = {Die {O}rdnung der {S}chafarewitsch-{T}ate-{G}ruppe kann
775
beliebig gro\ss \ werden},
776
journal = {Math. Nachr.},
777
volume = {67},
778
year = {1975},
779
pages = {157--179},
780
mrclass = {14K15},
781
mrnumber = {52 \#5684},
782
mrreviewer = {J. W. S. Cassels}
783
}
784
785
@Proceedings{ boston,
786
title = {Modular forms and \protect{F}ermat's last theorem
787
(Boston,MA, 1995)},
788
editor = {Cornell, G. and Silverman, J.\thinspace{}H. and Stevens,
789
G.},
790
note = {Papers from the Instructional Conference on Number Theory
791
and Arithmetic Geometry held at Boston University, Boston,
792
MA, August 9--18, 1995},
793
publisher = {Springer-Verlag},
794
address = {New York},
795
year = {1997},
796
pages = {xx+582},
797
isbn = {0-387-94609-8}
798
}
799
800
@Article{ boston-lenstra-ribet,
801
author = {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.} and
802
K.\thinspace{}A. Ribet},
803
title = {Quotients of group rings arising from two-dimensional
804
representations},
805
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
806
fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
807
Math\'ematique},
808
volume = {312},
809
year = {1991},
810
number = {4},
811
pages = {323--328},
812
issn = {0764-4442},
813
coden = {CASMEI}
814
}
815
816
@Article{ breuil-conrad-diamond-taylor,
817
author = {Breuil, C. and Conrad, B. and Diamond, F. and Taylor, R.},
818
title = {On the modularity of elliptic curves over {$\bold Q$}:
819
wild 3-adic exercises},
820
journal = {J. Amer. Math. Soc.},
821
fjournal = {Journal of the American Mathematical Society},
822
volume = {14},
823
year = {2001},
824
number = {4},
825
pages = {843--939 (electronic)},
826
issn = {0894-0347},
827
mrclass = {11G05 (11F80 11G07 14G35)},
828
mrnumber = {2002d:11058},
829
mrreviewer = {Karl Rubin}
830
}
831
832
@Article{ brue,
833
author = {Brueggeman, S.},
834
title = {The non-existence of certain \protect{Galois} extensions
835
unramified outside 5},
836
journal = {Journal of Number Theory},
837
volume = {75},
838
year = {1999},
839
pages = {47--52}
840
}
841
842
@Article{ brumer-mcguinness,
843
author = {Brumer, A. and McGuinness, O.},
844
title = {The behavior of the {M}ordell-{W}eil group of elliptic
845
curves},
846
journal = {Bull. Amer. Math. Soc. (N.S.)},
847
fjournal = {American Mathematical Society. Bulletin. New Series},
848
volume = {23},
849
year = {1990},
850
number = {2},
851
pages = {375--382},
852
issn = {0273-0979},
853
coden = {BAMOAD},
854
mrclass = {11G40 (11-04 11G05)},
855
mrnumber = {91b:11076},
856
mrreviewer = {Kenneth Kramer},
857
note = {\protect{\tt http://shimura.math.berkeley.edu/\~{ }oisin/}}
858
}
859
860
@Article{ brumer:rank,
861
author = {Brumer, A.},
862
title = {The rank of \protect{${J}\sb 0({N})$}},
863
note = {Columbia University Number Theory Seminar (New York,
864
1992)},
865
journal = {Ast\'erisque},
866
fjournal = {Ast\'erisque},
867
number = {228},
868
year = {1995},
869
pages = {3, 41--68},
870
issn = {0303-1179}
871
}
872
873
@Article{ buhler-gross,
874
author = {Buhler, J.\thinspace{}P. and Gross, B.\thinspace{}H.},
875
title = {Arithmetic on elliptic curves with complex multiplication.
876
{I}{I}},
877
journal = {Invent. Math.},
878
fjournal = {Inventiones Mathematicae},
879
volume = {79},
880
year = {1985},
881
number = {1},
882
pages = {11--29},
883
issn = {0020-9910},
884
coden = {INVMBH},
885
mrclass = {11G40 (11G05 14K22)},
886
mrnumber = {86j:11066},
887
mrreviewer = {Kenneth Kramer}
888
}
889
890
@Book{ buhler:thesis,
891
author = {Buhler, J.\thinspace{}P.},
892
title = {Icosahedral \protect{G}alois representations},
893
note = {Lecture Notes in Mathematics, Vol. 654},
894
publisher = {Springer-Verlag},
895
address = {Berlin},
896
year = {1978},
897
pages = {ii+143},
898
isbn = {3-540-08844-X}
899
}
900
901
@Article{ bump-friedberg-hoffstein,
902
author = {Bump, D. and Friedberg, S. and Hoffstein, J.},
903
title = {Eisenstein series on the metaplectic group and
904
nonvanishing theorems for automorphic
905
\protect{${L}$}-functions and their derivatives},
906
journal = {Ann. of Math. (2)},
907
fjournal = {Annals of Mathematics. Second Series},
908
volume = {131},
909
year = {1990},
910
number = {1},
911
pages = {53--127},
912
issn = {0003-486X},
913
coden = {ANMAAH}
914
}
915
916
@Article{ buzzard-stein:artin,
917
author = {Buzzard, K. and Stein, W.\thinspace{}A.},
918
title = {A mod five approach to modularity of icosahedral {G}alois
919
representations},
920
journal = {Pacific J. Math.},
921
fjournal = {Pacific Journal of Mathematics},
922
volume = {203},
923
year = {2002},
924
number = {2},
925
pages = {265--282},
926
issn = {0030-8730},
927
coden = {PJMAAI},
928
mrclass = {11F80},
929
mrnumber = {2003c:11052},
930
mrreviewer = {Mark Edward Tristan Dickinson}
931
}
932
933
@Article{ buzzard-taylor,
934
author = {Buzzard, K. and Taylor, R.},
935
title = {Companion forms and weight one forms},
936
journal = {Ann. of Math. (2)},
937
fjournal = {Annals of Mathematics. Second Series},
938
volume = {149},
939
year = {1999},
940
number = {3},
941
pages = {905--919},
942
issn = {0003-486X},
943
coden = {ANMAAH},
944
mrclass = {11Fxx},
945
mrnumber = {1 709 306}
946
}
947
948
@Article{ buzzard:level,
949
author = {Buzzard, K.},
950
title = {On level-lowering for mod 2 representations},
951
journal = {preprint}
952
}
953
954
@Article{ buzzard:t2,
955
author = {Buzzard, Kevin},
956
title = {On the eigenvalues of the {H}ecke operator {$T\sb 2$}},
957
journal = {J. Number Theory},
958
fjournal = {Journal of Number Theory},
959
volume = {57},
960
year = {1996},
961
number = {1},
962
pages = {130--132},
963
issn = {0022-314X},
964
coden = {JNUTA9},
965
mrclass = {11F25},
966
mrnumber = {96m:11033},
967
mrreviewer = {Thomas R. Shemanske}
968
}
969
970
@Article{ carayol:modell,
971
author = {Carayol, H.},
972
title = {Sur les \protect{repr\'esentations} galoisiennes modulo
973
\protect{$\ell$ attach\'ees} aux formes modulaires},
974
journal = {Duke Math. J.},
975
volume = {59},
976
year = {1989},
977
pages = {785--801}
978
}
979
980
@Article{ carearly,
981
author = "Carayol, H.",
982
title = {Sur les \protect{repr\'esentations}
983
\protect{$\ell$-adiques} \protect{associ\'ees} aux formes
984
modulaires de \protect{Hilbert}},
985
journal = {Ann. scient. \protect{\'Ec.} Norm. Sup., \protect{$4^{\rm
986
eb}$ s\'erie}},
987
volume = {19},
988
year = {1986},
989
pages = {409--468}
990
}
991
992
@InProceedings{ casselman,
993
author = {Casselman, W.},
994
title = {On representations of \protect{${\rm {G}{L}}\sb{2}$} and
995
the arithmetic of modular curves},
996
booktitle = {Modular functions of one variable, II (Proc. Internat.
997
Summer School, Univ. Antwerp, Antwerp, 1972)},
998
pages = {107--141. Lecture Notes in Math., Vol. 349},
999
publisher = {Springer},
1000
address = {Berlin},
1001
year = {1973}
1002
}
1003
1004
@Book{ cassels-flynn,
1005
author = {Cassels, J.\thinspace{}W.\thinspace{}S. and Flynn,
1006
E.\thinspace{}V.},
1007
title = {Prolegomena to a middlebrow arithmetic of curves of genus
1008
\protect{$2$}},
1009
publisher = {Cambridge University Press},
1010
address = {Cambridge},
1011
year = {1996},
1012
pages = {xiv+219},
1013
isbn = {0-521-48370-0},
1014
mrclass = {11G30 (11Y50 14G25)},
1015
mrnumber = {97i:11071},
1016
mrrevr = {Joseph H. Silverman}
1017
}
1018
1019
@Proceedings{ cassels-frohlich,
1020
title = {Algebraic number theory},
1021
booktitle = {Proceedings of the instructional conference held at the
1022
University of Sussex, Brighton, September 1--17, 1965},
1023
editor = {Cassels, J.\thinspace{}W.\thinspace{}S. and
1024
\protect{Fr{\"o}hlich}, A.},
1025
note = {Reprint of the 1967 original},
1026
publisher = {Academic Press Inc. [Harcourt Brace Jovanovich
1027
Publishers]},
1028
address = {London},
1029
year = {1986},
1030
pages = {xviii+366},
1031
isbn = {0-12-163251-2}
1032
}
1033
1034
@Article{ cassels:arithmeticiii,
1035
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
1036
title = {{A}rithmetic on curves of genus $1$. {I}{I}{I}. {T}he
1037
{T}ate-\v {S}afarevi\v c and {S}elmer groups},
1038
journal = {Proc. London Math. Soc. (3)},
1039
volume = {12},
1040
year = {1962},
1041
pages = {259--296},
1042
mrclass = {14.49},
1043
mrnumber = {29 \#1212}
1044
}
1045
1046
@Article{ cassels:arithmeticiv,
1047
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
1048
title = {Arithmetic on curves of genus \protect{$1$}. {I}{V}.
1049
{P}roof of the {H}auptvermutung},
1050
journal = {J. Reine Angew. Math.},
1051
volume = {211},
1052
year = {1962},
1053
pages = {95--112}
1054
}
1055
1056
@Article{ cassels:arithmeticv,
1057
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
1058
title = {Arithmetic on curves of genus 1. {V}. {T}wo
1059
counterexamples},
1060
journal = {J. London Math. Soc.},
1061
volume = {38},
1062
year = {1963},
1063
pages = {244--248}
1064
}
1065
1066
@Article{ cassels:bigsha,
1067
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
1068
title = {Arithmetic on curves of genus $1$. {V}{I}. {T}he {T}ate-\v
1069
{S}afarevi\v c group can be arbitrarily large},
1070
journal = {J. Reine Angew. Math.},
1071
volume = {214/215},
1072
year = {1964},
1073
pages = {65--70},
1074
mrclass = {14.49 (10.12)},
1075
mrnumber = {29 \#104},
1076
mrreviewer = {P. Abellanas}
1077
}
1078
1079
@Article{ cassels:diophantinecurve,
1080
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
1081
title = {Diophantine equations with special reference to elliptic
1082
curves},
1083
journal = {J. London Math. Soc.},
1084
volume = {41},
1085
year = {1966},
1086
pages = {193--291}
1087
}
1088
1089
@InCollection{ cassels:global,
1090
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
1091
title = {Global fields},
1092
booktitle = {Algebraic Number Theory (Proc. Instructional Conf.,
1093
Brighton, 1965)},
1094
pages = {42--84},
1095
publisher = {Thompson, Washington, D.C.},
1096
year = {1967}
1097
}
1098
1099
@Article{ cerednik,
1100
author = {{\v{C}}erednik, I.\thinspace{}V.},
1101
title = {Uniformization of algebraic curves by discrete arithmetic
1102
subgroups of \protect{${\rm {P}{G}{L}}\sb{2}(k\sb{w})$}
1103
with compact quotient spaces},
1104
journal = {Mat. Sb. (N.S.)},
1105
volume = {100(142)},
1106
year = {1976},
1107
number = {1},
1108
pages = {59--88, 165}
1109
}
1110
1111
@Article{ cheryl,
1112
author = {Beaver, Cheryl DeLorme},
1113
title = {$5$-torsion in the {S}hafarevich-{T}ate group of a family
1114
of elliptic curves},
1115
journal = {J. Number Theory},
1116
fjournal = {Journal of Number Theory},
1117
volume = {82},
1118
year = {2000},
1119
number = {1},
1120
pages = {25--46},
1121
issn = {0022-314X},
1122
coden = {JNUTA9},
1123
mrclass = {11G05 (11G07)},
1124
mrnumber = {2001d:11059},
1125
mrreviewer = {Kenneth Kramer}
1126
}
1127
1128
@Article{ chevalley:thm,
1129
author = {Chevalley, C.},
1130
title = {Une d\'emonstration d'un th\'eor\`eme sur les groupes
1131
alg\'ebriques},
1132
journal = {J. Math. Pures Appl. (9)},
1133
volume = {39},
1134
year = {1960},
1135
pages = {307--317},
1136
mrclass = {14.50},
1137
mrnumber = {23 \#A3743},
1138
mrreviewer = {I. Barsotti}
1139
}
1140
1141
@Book{ cime-1997,
1142
author = "Viola, C.",
1143
title = "{Arithmetic theory of elliptic curves. Lectures given at
1144
the 3rd session of the {C}entro {I}nternazionale
1145
{M}atematico {E}stivo \protect{(CIME)}.}",
1146
language = "English",
1147
source = "{{L}ecture {N}otes in {M}athematics. 1716. {B}erlin:
1148
{S}pringer. viii, 260 p. DM 74.00; oeS 541.00; sFr. 67.50;
1149
\sterling 28.50; \$ 52.80 (1999). [ISBN 3-540-66546-3/hbk;
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ISSN 0075-8434]}",
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}
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title = {Millennium Prize Problems,\hfill\\{\tt
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@Article{ coleman-stein:padicapprox,
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@Article{ coleman:banach,
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}
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@Article{ coleman:classical,
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@Article{ coleman:classical_higher,
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@Article{ coleman:monodromy,
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1315
1316
@Article{ colmez_fontaine,
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author = {Colmez, P. and Fontaine, J.-M.},
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title = {Construction des repr\'esentations {$p$}-adiques
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@Article{ conrad-diamond-taylor:modularity,
1334
author = {Conrad, B. and Diamond, F. and Taylor, R.},
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title = {Modularity of certain potentially
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\protect{B}arsotti-\protect{T}ate \protect{G}alois
1337
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1338
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1342
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1345
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@Article{ conrad-edixhoven-stein:j1p,
1348
author = {Conrad, B. and Edixhoven, S. and Stein, W.\thinspace{}A.},
1349
title = {${J}_1(p)$ {H}as {C}onnected {F}ibers},
1350
year = 2003,
1351
journal = {Documenta Mathematica},
1352
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1354
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@Article{ conrad-stein:compgroup,
1357
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1358
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1369
}
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1371
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1372
author = {Conrad, K.},
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title = {{P}artial {E}uler products on the critical line},
1374
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year = {2003}
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}
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@InCollection{ conrad:shimura,
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author = {Conrad, B.},
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title = {The Shimura Construction in Weight 2 (appendix to
1381
{R}ibet-{S}tein, {L}ectures on {S}erre's {C}onjecture)},
1382
booktitle = {Arithmetic algebraic geometry (Park City, UT, 1999)},
1383
series = {IAS/Park City Math. Ser.},
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1388
year = {2001},
1389
mrclass = {11F80 (11F66 11G05)},
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mrnumber = {2002h:11047}
1391
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@InCollection{ conrey-farmer:nonvanish,
1394
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1395
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1397
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@Article{ cremona-luiz,
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1410
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1411
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1412
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1414
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1415
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@Article{ cremona:gammaone,
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@Article{ cremona:onlinetables,
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author = {Cremona, J.\thinspace{}E.},
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title = {Elliptic curves of conductor \protect{$\leq
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@Article{ cremona:periods,
1463
author = {Cremona, J.\thinspace{}E.},
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1465
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1466
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@Book{ curtis-reiner,
1476
author = {Curtis, C.\thinspace{}W. and Reiner, I.},
1477
title = {Representation theory of finite groups and associative
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year = {1962},
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pages = {xiv+685}
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@InCollection{ darmon-bsd,
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booktitle = {Modular forms and Fermat's last theorem (Boston, MA,
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author = {Darmon, H. and Merel, L.},
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mrnumber = {98h:11076},
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mrrevr = {Kenneth Kramer}
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@InCollection{ darmon:serre,
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title = {Serre's conjectures},
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booktitle = {Seminar on Fermat's Last Theorem (Toronto, ON,
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@InCollection{ ddt,
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booktitle = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
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address = {Berlin and New York},
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year = {1971},
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pages = {139--172}
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@InProceedings{ deligne-rapoport,
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author = {Deligne, P. and Rapoport, M.},
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title = {Les sch\'emas de modules de courbes elliptiques},
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booktitle = {Modular functions of one variable, II (Proc. Internat.
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Summer School, Univ. Antwerp, Antwerp, 1972)},
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address = {Berlin},
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@Article{ deligne-serre,
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title = {Modular forms and modular curves},
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booktitle = {Seminar on {F}ermat's {L}ast {T}heorem},
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@Article{ diamond-kramer,
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@Article{ dickinson:thesis,
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title = {\protect{${S}\sb 4$} and \protect{$\tilde {S}{}\sb 4$}
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@Article{ drinfeld:coverings,
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title = {{Constructing Elements in Shafarevich-Tate Groups of
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Modular Motives}},
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@Article{ dummigan:cp,
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author = {Dummigan, N.},
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journal = {to appear in Math. Annalen}
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@Article{ edixcole,
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@Article{ edixhoven:comparison,
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@Article{ edixhoven:eisen,
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de composantes des jacobiennes des courbes modulaires est
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title = {On the {M}anin constants of modular elliptic curves},
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title = {Le r\^{o}le de la conjecture de {S}erre dans la
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\'{E}tude locale des sch\'emas et des morphismes de
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\'{E}tude locale des sch\'emas et des morphismes de
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\'{E}tude locale des sch\'emas et des morphismes de
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booktitle = {Galois representations in arithmetic algebraic geometry
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@Book{ eisenbud-harris-2,
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@InCollection{ elkies:ffield,
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title = {Elliptic and modular curves over finite fields and related
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http://www.math.princeton.edu/~ellenber/papers.html\#QCURVE}}
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journal = {{\tt
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http://www.math.princeton.edu/~ellenber/papers.html\#MCAV}},
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title = {Empirical evidence for the {B}irch and {S}winnerton-{D}yer
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conjectures for modular {J}acobians of genus 2 curves},
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mrrevr = {Glenn Stevens}
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@Article{ goldfeld:l1,
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2220
title = {Sur les produits partiels eul\'eriens attach\'es aux
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author = {Gonz{\'a}lez, J. and Lario, J.-C.},
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title = {{$\mathbf{Q}$}-curves and their {M}anin ideals},
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@Article{ gordon-ono:vis,
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title = {Modular form {C}ongruences and {S}elmer groups},
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@InCollection{ gouvea-mazur:density,
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mrreviewer = {Andrea Mori}
2271
}
2272
2273
@Article{ gouvea-mazur:families,
2274
author = {Gouv\^ea, F. and Mazur, B.},
2275
title = {Families of modular eigenforms},
2276
journal = {Math. Comp.},
2277
fjournal = {Mathematics of Computation},
2278
volume = {58},
2279
year = {1992},
2280
number = {198},
2281
pages = {793--805},
2282
issn = {0025-5718},
2283
coden = {MCMPAF},
2284
mrclass = {11F33 (11Y35 14G20)},
2285
mrnumber = {93d:11049},
2286
mrrevr = {Bas Edixhoven}
2287
}
2288
2289
@Article{ gouvea:ordinary,
2290
author = {Gouv\^ea, F.\thinspace{}Q.},
2291
title = {On the ordinary {H}ecke algebra},
2292
journal = {J. Number Theory},
2293
fjournal = {Journal of Number Theory},
2294
volume = {41},
2295
year = {1992},
2296
number = {2},
2297
pages = {178--198},
2298
issn = {0022-314X},
2299
coden = {JNUTA9}
2300
}
2301
2302
@Book{ gouvea:slnm,
2303
author = {Gouv\^{e}a, F.\thinspace{}Q.},
2304
title = {Arithmetic of $p$-adic modular forms},
2305
publisher = {Springer-Verlag},
2306
address = {Berlin},
2307
year = {1988},
2308
pages = {viii+121},
2309
isbn = {3-540-18946-7},
2310
mrclass = {11F85 (11F80)},
2311
mrnumber = {91e:11056},
2312
mrreviewer = {Alexey A. Panchishkin}
2313
}
2314
2315
@Book{ greenberg-harper,
2316
author = {Greenberg, M.\thinspace{}J. and Harper, J.\thinspace{}R.},
2317
title = {Algebraic topology},
2318
note = {A first course},
2319
publisher = {Benjamin/Cummings Publishing Co. Inc. Advanced Book
2320
Program},
2321
address = {Reading, Mass.},
2322
year = {1981},
2323
pages = {xi+311 pp. (loose errata)},
2324
isbn = {0-8053-3558-7; 0-8053-3557-9},
2325
mrclass = {55-01},
2326
mrnumber = {83b:55001},
2327
mrrevr = {J. P. May}
2328
}
2329
2330
@Article{ gross-kohnen-zagier,
2331
author = {Gross, B. and Kohnen, W. and Zagier, D.},
2332
title = {Heegner points and derivatives of ${L}$-series. {I}{I}},
2333
journal = {Math. Ann.},
2334
fjournal = {Mathematische Annalen},
2335
volume = {278},
2336
year = {1987},
2337
number = {1-4},
2338
pages = {497--562},
2339
issn = {0025-5831},
2340
coden = {MAANA3},
2341
mrclass = {11G40 (11F30 11G05 11R29 14G10)},
2342
mrnumber = {89i:11069},
2343
mrrevr = {Lawrence Washington}
2344
}
2345
2346
@Article{ gross-zagier,
2347
author = {Gross, B. and Zagier, D.},
2348
title = {Heegner points and derivatives of \protect{${L}$}-series},
2349
journal = {Invent. Math.},
2350
fjournal = {Inventiones Mathematicae},
2351
volume = {84},
2352
year = {1986},
2353
number = {2},
2354
pages = {225--320},
2355
issn = {0020-9910},
2356
coden = {INVMBH},
2357
mrclass = {11G40 (11F11 11G05 14G10)},
2358
mrnumber = {87j:11057},
2359
mrrevr = {Loren D. Olson}
2360
}
2361
2362
@InCollection{ gross:central,
2363
author = {Gross, B.\thinspace{}H.},
2364
title = {${L}$-functions at the central critical point},
2365
booktitle = {Motives (Seattle, WA, 1991)},
2366
pages = {527--535},
2367
publisher = {Amer. Math. Soc.},
2368
address = {Providence, RI},
2369
year = {1994},
2370
mrclass = {11G40 (14G10)},
2371
mrnumber = {95a:11060},
2372
mrrevr = {Jan Nekov{\'a}{\v{r}}}
2373
}
2374
2375
@InCollection{ gross:kolyvagin,
2376
author = {Gross, B.\thinspace{}H.},
2377
title = {Kolyvagin's work on modular elliptic curves},
2378
booktitle = {$L$-functions and arithmetic (Durham, 1989)},
2379
pages = {235--256},
2380
publisher = {Cambridge Univ. Press},
2381
address = {Cambridge},
2382
year = {1991}
2383
}
2384
2385
@Article{ gross:tameness,
2386
author = {Gross, B.\thinspace{}H.},
2387
title = {A tameness criterion for \protect{G}alois representations
2388
associated to modular forms (mod \protect{$p$})},
2389
journal = {Duke Math. J.},
2390
fjournal = {Duke Mathematical Journal},
2391
volume = {61},
2392
year = {1990},
2393
number = {2},
2394
pages = {445--517},
2395
issn = {0012-7094},
2396
coden = {DUMJAO}
2397
}
2398
2399
@Article{ gross_kudla,
2400
author = {Gross, B.\thinspace{}H. and Kudla, S.\thinspace{}S.},
2401
title = {Heights and the central critical values of triple product
2402
{$L$}-functions},
2403
journal = {Compositio Math.},
2404
fjournal = {Compositio Mathematica},
2405
volume = {81},
2406
year = {1992},
2407
number = {2},
2408
pages = {143--209},
2409
issn = {0010-437X},
2410
coden = {CMPMAF},
2411
mrclass = {11F66 (11F67 11G40 19F27)},
2412
mrnumber = {93g:11047},
2413
mrreviewer = {Alexey A. Panchishkin}
2414
}
2415
2416
@InCollection{ grothendieck:brauer1,
2417
author = {Grothendieck, Alexander},
2418
title = {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et
2419
interpr\'etations diverses},
2420
booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
2421
pages = {46--66},
2422
publisher = {North-Holland},
2423
address = {Amsterdam},
2424
year = {1968},
2425
mrclass = {14.55},
2426
mrnumber = {39 #5586a}
2427
}
2428
2429
@InCollection{ grothendieck:brauer2,
2430
author = {Grothendieck, Alexander},
2431
title = {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique},
2432
booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
2433
pages = {67--87},
2434
publisher = {North-Holland},
2435
address = {Amsterdam},
2436
year = {1968},
2437
mrclass = {14.55},
2438
mrnumber = {39 #5586b}
2439
}
2440
2441
@InCollection{ grothendieck:brauer3,
2442
author = {Grothendieck, Alexander},
2443
title = {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et
2444
compl\'ements},
2445
booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
2446
pages = {88--188},
2447
publisher = {North-Holland},
2448
address = {Amsterdam},
2449
year = {1968},
2450
mrclass = {14.55},
2451
mrnumber = {39 #5586c},
2452
mrrevr = {J. S. Milne}
2453
}
2454
2455
@Book{ grothendieck:monodromie,
2456
author = {Grothendieck, A.},
2457
title = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique.
2458
\protect{I}},
2459
note = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
2460
1967--1969 (SGA 7 I), Dirig\'e par A. Grothendieck. Avec la
2461
collaboration de M. Raynaud et D. S. Rim, Lecture Notes in
2462
Mathematics, Vol. 288},
2463
publisher = {Springer-Verlag},
2464
address = {Berlin},
2465
year = {1972},
2466
pages = {viii+523}
2467
}
2468
2469
@InCollection{ gruenberg,
2470
author = {Gruenberg, K.},
2471
title = {Profinite groups},
2472
booktitle = {Algebraic Number Theory (Proc. Instructional Conf.,
2473
Brighton, 1965)},
2474
pages = {116--127},
2475
publisher = {Thompson, Washington, D.C.},
2476
year = {1967}
2477
}
2478
2479
@Article{ guerzhoy:kummer,
2480
title = {Searching for {K}ummer congruences in an infinite slope
2481
family},
2482
author = {Guerzhoy, P.},
2483
year = {2000},
2484
journal = {Preprint}
2485
}
2486
2487
@Book{ guy:unsolved,
2488
author = {Guy, R.\thinspace{}K.},
2489
title = {Unsolved problems in number theory},
2490
edition = {Second},
2491
note = {Unsolved Problems in Intuitive Mathematics, I},
2492
publisher = {Springer-Verlag},
2493
address = {New York},
2494
year = {1994},
2495
pages = {xvi+285},
2496
isbn = {0-387-94289-0},
2497
mrclass = {11-01 (00A07 11-02)},
2498
mrnumber = {96e:11002},
2499
mrreviewer = {B. M. M. de Weger}
2500
}
2501
2502
@Book{ haberland,
2503
author = {Haberland, Klaus},
2504
title = {Galois cohomology of algebraic number fields},
2505
note = {With two appendices by Helmut Koch and Thomas Zink},
2506
publisher = {VEB Deutscher Verlag der Wissenschaften},
2507
address = {Berlin},
2508
year = {1978},
2509
pages = {145},
2510
mrclass = {12A60},
2511
mrnumber = {81i:12009},
2512
mrrevr = {Chih-Han Sah}
2513
}
2514
2515
@Book{ halmos:naive,
2516
author = {Halmos, Paul R.},
2517
title = {Naive set theory},
2518
series = {The University Series in Undergraduate Mathematics},
2519
publisher = {D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New
2520
York},
2521
year = {1960},
2522
pages = {vii+104},
2523
mrclass = {04.00},
2524
mrnumber = {22 \#5575},
2525
mrreviewer = {L. Rieger}
2526
}
2527
2528
@Article{ hardy_littlewood:conjf,
2529
author = {Hardy, G.\thinspace{}H. and Littlewood, J.\thinspace{}E.},
2530
title = {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}.
2531
{O}n the {E}xpression of a {N}umber as a {S}um of
2532
{P}rimes.},
2533
journal = {Acta. Math.},
2534
volume = {44},
2535
year = {1922},
2536
pages = {1--70}
2537
}
2538
2539
@Book{ hartshorne,
2540
author = {Hartshorne, R.},
2541
title = {Algebraic {G}eometry},
2542
note = {Graduate Texts in Mathematics, No. 52},
2543
publisher = {Springer-Verlag},
2544
address = {New York},
2545
year = {1977},
2546
pages = {xvi+496},
2547
isbn = {0-387-90244-9}
2548
}
2549
2550
@Article{ hatada:eigenvalues79,
2551
author = {Hatada, K.},
2552
title = {Eigenvalues of {H}ecke operators on \protect{${\rm
2553
{S}{L}}(2,\,{\bf {Z}})$}},
2554
journal = {Math. Ann.},
2555
fjournal = {Mathematische Annalen},
2556
volume = {239},
2557
year = {1979},
2558
number = {1},
2559
pages = {75--96},
2560
issn = {0025-5831},
2561
coden = {MAANA3},
2562
mrclass = {10D15},
2563
mrnumber = {80b:10037},
2564
mrreviewer = {Roy Fuller}
2565
}
2566
2567
@Article{ hatada:general,
2568
author = {Hatada, K.},
2569
title = {On classical and {$l$}-adic modular forms of levels
2570
{$Nl\sp m$} and {$N$}},
2571
journal = {J. Number Theory},
2572
fjournal = {Journal of Number Theory},
2573
volume = {87},
2574
year = {2001},
2575
number = {1},
2576
pages = {1--14},
2577
issn = {0022-314X},
2578
coden = {JNUTA9},
2579
mrclass = {11F11 (11F80 11F85)},
2580
mrnumber = {2002e:11054},
2581
mrreviewer = {Luis V. Dieulefait}
2582
}
2583
2584
@Article{ hatada:rationality,
2585
author = {Hatada, K.},
2586
title = {Multiplicity one theorem and modular symbols},
2587
journal = {J. Math. Soc. Japan},
2588
fjournal = {Journal of the Mathematical Society of Japan},
2589
volume = {33},
2590
year = {1981},
2591
number = {3},
2592
pages = {445--470},
2593
issn = {0025-5645},
2594
coden = {NISUBC},
2595
mrclass = {10D12 (12A65)},
2596
mrnumber = {83d:10030},
2597
mrrevr = {Wen Ch'ing Winnie Li}
2598
}
2599
2600
@Book{ hellegouarch:invitation,
2601
author = {Hellegouarch, Y.},
2602
title = {Invitation aux math\'ematiques de {F}ermat-{W}iles},
2603
publisher = {Masson},
2604
address = {Paris},
2605
year = {1997},
2606
pages = {viii+401},
2607
isbn = {2-225-83008-8},
2608
mrclass = {11-01 (11D41 11F11 11G05 11G18)},
2609
mrnumber = {99e:11001},
2610
mrrevr = {Massimo Bertolini}
2611
}
2612
2613
@Article{ hida:invent86,
2614
author = {Hida, H.},
2615
title = {Galois representations into \protect{${\rm {G}{L}}\sb
2616
2({\bf {Z}}\sb p[[{X}]])$} attached to ordinary cusp forms},
2617
journal = {Invent. Math.},
2618
fjournal = {Inventiones Mathematicae},
2619
volume = {85},
2620
year = {1986},
2621
number = {3},
2622
pages = {545--613},
2623
issn = {0020-9910},
2624
coden = {INVMBH},
2625
mrclass = {11F11 (11F33 11F85 11R23)},
2626
mrnumber = {87k:11049},
2627
mrrevr = {Ernst-Wilhelm Zink}
2628
}
2629
2630
@Article{ hida:iwasawa,
2631
author = {Hida, H.},
2632
title = {Iwasawa modules attached to congruences of cusp forms},
2633
journal = {Ann. Sci. \'Ecole Norm. Sup. (4)},
2634
fjournal = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
2635
Quatri\`eme S\'erie},
2636
volume = {19},
2637
year = {1986},
2638
number = {2},
2639
pages = {231--273},
2640
issn = {0012-9593},
2641
coden = {ASENAH},
2642
mrclass = {11F33 (11G18 11R23)},
2643
mrnumber = {88i:11023},
2644
mrrevr = {Yasutaka Ihara}
2645
}
2646
2647
@Article{ hida:modularity,
2648
author = {Hida, H.},
2649
title = {Modularity {P}roblems of {$\Q$}-{M}otives and
2650
{B}ase-{C}hange},
2651
journal = {Preprint, {\tt http://www.math.ucla.edu/~hida/}},
2652
year = {2000}
2653
}
2654
2655
@Article{ hijikata:trace,
2656
author = {Hijikata, H.},
2657
title = {Explicit formula of the traces of \protect{H}ecke
2658
operators for \protect{$\Gamma_0(N)$}},
2659
journal = {J. Math. Soc. Japan},
2660
number = {1},
2661
volume = {26},
2662
year = {1974},
2663
pages = {56--82}
2664
}
2665
2666
@Book{ hindry-silverman:diophantine,
2667
author = {Hindry, Marc and Silverman, Joseph H.},
2668
title = {Diophantine geometry},
2669
note = {An introduction},
2670
publisher = {Springer-Verlag},
2671
address = {New York},
2672
year = {2000},
2673
pages = {xiv+558},
2674
isbn = {0-387-98975-7; 0-387-98981-1},
2675
mrclass = {11Gxx (11-02 11G10 11G30 11G50 14G25)},
2676
mrnumber = {2001e:11058},
2677
mrreviewer = {Dino J. Lorenzini}
2678
}
2679
2680
@InProceedings{ hpf,
2681
author = {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.},
2682
title = {On $\ell$-adic representations and congruences for
2683
coefficients of modular forms},
2684
booktitle = {Proceedings of the International Summer School, University
2685
of Antwerp, RUCA, July 17--August 3, 1972},
2686
pages = {1--55. Lecture Notes in Math., Vol. 350},
2687
publisher = {Springer},
2688
address = {Berlin},
2689
year = {1973}
2690
}
2691
2692
@Article{ igusa:fibre,
2693
author = {Igusa, J.},
2694
title = {Fibre systems of \protect{J}acobian varieties},
2695
journal = {Amer. J. Math.},
2696
volume = {78},
2697
year = {1956},
2698
pages = {171--199}
2699
}
2700
2701
@Book{ jacquet-langlands,
2702
author = {Jacquet, H. and Langlands, R.\thinspace{}P.},
2703
title = {Automorphic forms on \protect{${\rm {G}{L}}(2)$}},
2704
note = {Lecture Notes in Mathematics, Vol. 114},
2705
publisher = {Springer-Verlag},
2706
address = {Berlin},
2707
year = {1970},
2708
pages = {vii+548}
2709
}
2710
2711
@Article{ jarvis:hilbert,
2712
author = {Jarvis, F.},
2713
title = {On \protect{G}alois representations associated to
2714
\protect{H}ilbert modular forms},
2715
journal = {J. Reine Angew. Math.},
2716
fjournal = {Journal f\"ur die Reine und Angewandte Mathematik},
2717
volume = {491},
2718
year = {1997},
2719
pages = {199--216},
2720
issn = {0075-4102},
2721
coden = {JRMAA8}
2722
}
2723
2724
@Article{ jarvis:level,
2725
author = {Jarvis, F.},
2726
title = {Level lowering for modular mod \protect{$\ell$}
2727
representations over totally real fields\-},
2728
journal = {Math. Ann.},
2729
fjournal = {Mathematische Annalen},
2730
volume = {313},
2731
year = {1999},
2732
number = {1},
2733
pages = {141--160},
2734
issn = {0025-5831},
2735
coden = {MAANA}
2736
}
2737
2738
@Article{ jarvis:mazur,
2739
author = {Jarvis, F.},
2740
title = {Mazur's principle for totally real fields of odd degree},
2741
journal = {Compositio Math.},
2742
fjournal = {Compositio Mathematica},
2743
volume = {116},
2744
year = {1999},
2745
number = {1},
2746
pages = {39--79},
2747
issn = {0010-437X},
2748
coden = {CMPMAF}
2749
}
2750
2751
@InCollection{ jochnowitz:conjecture,
2752
author = {Jochnowitz, N.},
2753
title = {A $p$-adic conjecture about derivatives of ${L}$-series
2754
attached to modular forms},
2755
booktitle = {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
2756
conjecture},
2757
pages = {239--263},
2758
publisher = {Amer. Math. Soc.},
2759
address = {Providence, RI},
2760
year = {1994},
2761
mrclass = {11F33 (11F67 11F85 11G40)},
2762
mrnumber = {95g:11037},
2763
mrrevr = {Andrea Mori}
2764
}
2765
2766
@Article{ jochnowitz:duke,
2767
author = {Jochnowitz, N.},
2768
title = {The index of the {H}ecke ring, ${T}\sb{k}$, in the ring of
2769
integers of \protect{${T}\sb{k}\otimes {\bf {Q}}$}},
2770
journal = {Duke Math. J.},
2771
fjournal = {Duke Mathematical Journal},
2772
volume = {46},
2773
year = {1979},
2774
number = {4},
2775
pages = {861--869},
2776
issn = {0012-7094},
2777
coden = {DUMJAO},
2778
mrclass = {10D12},
2779
mrnumber = {80k:10023},
2780
mrrevr = {Henri Cohen}
2781
}
2782
2783
@Article{ jochnowitz:local,
2784
author = {Jochnowitz, N.},
2785
title = {A study of the local components of the \protect{H}ecke
2786
algebra mod \protect{$\ell$}},
2787
journal = {Trans. Amer. Math. Soc.},
2788
fjournal = {Transactions of the American Mathematical Society},
2789
volume = {270},
2790
year = {1982},
2791
number = {1},
2792
pages = {253--267},
2793
issn = {0002-9947},
2794
coden = {TAMTAM}
2795
}
2796
2797
@Article{ jones:thesis,
2798
author = {Jones, D.\thinspace{}M.},
2799
title = {On modular {G}alois representations in characteristic
2800
$3$},
2801
year = {1998},
2802
journal = {U.\thinspace{}C. Berkeley Ph.D. thesis}
2803
}
2804
2805
@Article{ jordan-livne:epsilon,
2806
author = {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
2807
title = {Conjecture ``epsilon'' for weight \protect{$k>2$}},
2808
journal = {Bull. Amer. Math. Soc. (N.S.)},
2809
fjournal = {American Mathematical Society. Bulletin. New Series},
2810
volume = {21},
2811
year = {1989},
2812
number = {1},
2813
pages = {51--56},
2814
issn = {0273-0979},
2815
coden = {BAMOAD}
2816
}
2817
2818
@Article{ jordan-livne:sha,
2819
author = {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
2820
title = {On {A}tkin-{L}ehner quotients of {S}himura curves},
2821
journal = {Bull. London Math. Soc.},
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fjournal = {The Bulletin of the London Mathematical Society},
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2831
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2832
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2848
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2849
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2853
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2856
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2858
2859
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2860
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2862
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2865
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2866
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2868
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2869
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2870
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2871
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2874
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