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Author: William A. Stein
1
@incollection{conrad:shimura,
2
AUTHOR = {Conrad, B.},
3
TITLE = {The Shimura Construction in Weight 2 (appendix to {R}ibet-{S}tein,
4
{L}ectures on {S}erre's {C}onjecture)},
5
BOOKTITLE = {Arithmetic algebraic geometry (Park City, UT, 1999)},
6
SERIES = {IAS/Park City Math. Ser.},
7
VOLUME = {9},
8
PAGES = {205--232},
9
PUBLISHER = {Amer. Math. Soc.},
10
ADDRESS = {Providence, RI},
11
YEAR = {2001},
12
MRCLASS = {11F80 (11F66 11G05)},
13
MRNUMBER = {2002h:11047},
14
}
15
16
@article {agashe:invisible,
17
AUTHOR = {Agash{\'e}, Amod},
18
TITLE = {On invisible elements of the {T}ate-{S}hafarevich group},
19
JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
20
FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
21
Math\'ematique},
22
VOLUME = {328},
23
YEAR = {1999},
24
NUMBER = {5},
25
PAGES = {369--374},
26
ISSN = {0764-4442},
27
CODEN = {CASMEI},
28
MRCLASS = {11G40 (11G10 11G18)},
29
MRNUMBER = {2000e:11083},
30
MRREVIEWER = {Kenneth Kramer},
31
}
32
33
@article {ogg:ratpoints,
34
AUTHOR = {Ogg, A.\thinspace{}P.},
35
TITLE = {Rational points of finite order on elliptic curves},
36
JOURNAL = {Invent. Math.},
37
VOLUME = {12},
38
YEAR = {1971},
39
PAGES = {105--111},
40
MRCLASS = {10D05},
41
MRNUMBER = {45 \#178},
42
MRREVIEWER = {K. Mahler}
43
}
44
45
@article {farmer-james:maeda,
46
AUTHOR = {Farmer, D. W. and James, K.},
47
TITLE = {The irreducibility of some level 1 {H}ecke polynomials},
48
JOURNAL = {Math. Comp.},
49
FJOURNAL = {Mathematics of Computation},
50
VOLUME = {71},
51
YEAR = {2002},
52
NUMBER = {239},
53
PAGES = {1263--1270 (electronic)},
54
ISSN = {0025-5718},
55
CODEN = {MCMPAF},
56
MRCLASS = {11F25 (11F11)},
57
MRNUMBER = {2003e:11046},
58
MRREVIEWER = {T. C. Vasudevan}
59
}
60
61
@article {buzzard:t2,
62
AUTHOR = {Buzzard, Kevin},
63
TITLE = {On the eigenvalues of the {H}ecke operator {$T\sb 2$}},
64
JOURNAL = {J. Number Theory},
65
FJOURNAL = {Journal of Number Theory},
66
VOLUME = {57},
67
YEAR = {1996},
68
NUMBER = {1},
69
PAGES = {130--132},
70
ISSN = {0022-314X},
71
CODEN = {JNUTA9},
72
MRCLASS = {11F25},
73
MRNUMBER = {96m:11033},
74
MRREVIEWER = {Thomas R. Shemanske}
75
}
76
77
@book {swinnerton-dyer:abvars,
78
AUTHOR = {Swinnerton-Dyer, H. P. F.},
79
TITLE = {Analytic theory of abelian varieties},
80
NOTE = {London Mathematical Society Lecture Note Series, No. 14},
81
PUBLISHER = {Cambridge University Press},
82
ADDRESS = {London},
83
YEAR = {1974},
84
PAGES = {viii+90},
85
MRCLASS = {14K20},
86
MRNUMBER = {51 \#3180},
87
MRREVIEWER = {H. Klingen},
88
}
89
90
91
@article {mazur-swinnerton-dyer:arithmetic,
92
AUTHOR = {Mazur, B. and Swinnerton-Dyer, P.},
93
TITLE = {Arithmetic of {W}eil curves},
94
JOURNAL = {Invent. Math.},
95
VOLUME = {25},
96
YEAR = {1974},
97
PAGES = {1--61},
98
MRCLASS = {14G05 (10D05)},
99
MRNUMBER = {50 \#7152},
100
MRREVIEWER = {J. S. Milne}
101
}
102
103
104
105
106
@incollection {ogg:ratpoints,
107
AUTHOR = {Ogg, A. P.},
108
TITLE = {Rational points on certain elliptic modular curves},
109
BOOKTITLE = {Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV,
110
St. Louis Univ., St. Louis, Mo., 1972)},
111
PAGES = {221--231},
112
PUBLISHER = {Amer. Math. Soc.},
113
ADDRESS = {Providence, R.I.},
114
YEAR = {1973},
115
MRCLASS = {14G05 (10D05 14K15)},
116
MRNUMBER = {49 \#2743},
117
MRREVIEWER = {J. W. S. Cassels}
118
}
119
120
@book {MR48:5967,
121
TITLE = {Analytic number theory},
122
BOOKTITLE = {Proceedings of the Symposium in Pure Mathematics of the
123
American Mathematical Society, held at St. Louis University,
124
St. Louis, Mo., March 27--30, 1972},
125
EDITOR = {Diamond, Harold G.},
126
BOOKTITLE = {Proceedings of Symposia in Pure Mathematics, Vol. XXIV},
127
PUBLISHER = {American Mathematical Society},
128
ADDRESS = {Providence, R.I.},
129
YEAR = {1973},
130
PAGES = {xii+340},
131
MRCLASS = {10-06},
132
MRNUMBER = {48 \#5967}
133
}
134
135
136
137
@article {ribet:twistsendoalg,
138
AUTHOR = {Ribet, K.\thinspace{}A.},
139
TITLE = {Twists of modular forms and endomorphisms of abelian
140
varieties},
141
JOURNAL = {Math. Ann.},
142
FJOURNAL = {Mathematische Annalen},
143
VOLUME = {253},
144
YEAR = {1980},
145
NUMBER = {1},
146
PAGES = {43--62},
147
ISSN = {0025-5831},
148
CODEN = {MAANA3},
149
MRCLASS = {10D15 (14G13)},
150
MRNUMBER = {82e:10043},
151
MRREVIEWER = {Wen Ch'ing Winnie Li}
152
}
153
154
@incollection {ribet:endalg,
155
AUTHOR = {Ribet, K. A.},
156
TITLE = {Endomorphism algebras of abelian varieties attached to
157
newforms of weight {$2$}},
158
BOOKTITLE = {Seminar on Number Theory, Paris 1979--80},
159
SERIES = {Progr. Math.},
160
VOLUME = {12},
161
PAGES = {263--276},
162
PUBLISHER = {Birkh\"auser Boston},
163
ADDRESS = {Mass.},
164
YEAR = {1981},
165
MRCLASS = {10D15 (14G13)},
166
MRNUMBER = {82m:10044},
167
MRREVIEWER = {Wen Ch'ing Winnie Li}
168
}
169
170
@book {MR82j:10004,
171
TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1979--80},
172
SERIES = {Progress in Mathematics},
173
VOLUME = {12},
174
EDITOR = {Bertin, Marie-Jos{\'e}},
175
NOTE = {S\'eminaire Delange-Pisot-Poitou. [Delange-Pisot-Poitou
176
Seminar],
177
Held in Paris, 1979--80},
178
PUBLISHER = {Birkh\"auser Boston},
179
ADDRESS = {Mass.},
180
YEAR = {1981},
181
PAGES = {ix+394},
182
ISBN = {3-7643-3035-X},
183
MRCLASS = {10-06},
184
MRNUMBER = {82j:10004}
185
}
186
187
188
189
@incollection {ribet:torsionj0,
190
AUTHOR = {Ribet, K.\thinspace{}A.},
191
TITLE = {Torsion points on {$J\sb 0(N)$} and {G}alois representations},
192
BOOKTITLE = {Arithmetic theory of elliptic curves (Cetraro, 1997)},
193
SERIES = {Lecture Notes in Math.},
194
VOLUME = {1716},
195
PAGES = {145--166},
196
PUBLISHER = {Springer},
197
ADDRESS = {Berlin},
198
YEAR = {1999},
199
MRCLASS = {11G18 (11F80)},
200
MRNUMBER = {2001b:11054},
201
MRREVIEWER = {Matthew H. Baker}
202
}
203
204
@book {MR2000m:11002,
205
AUTHOR = {Coates, J. and Greenberg, R. and Ribet, K. A. and Rubin, K.},
206
TITLE = {Arithmetic theory of elliptic curves},
207
SERIES = {Lecture Notes in Mathematics},
208
VOLUME = {1716},
209
NOTE = {Lectures from the 3rd C.I.M.E.\ Session held in Cetraro, July
210
12--19, 1997,
211
Edited by C. Viola},
212
PUBLISHER = {Springer-Verlag},
213
ADDRESS = {Berlin},
214
YEAR = {1999},
215
PAGES = {viii+234},
216
ISBN = {3-540-66546-3},
217
MRCLASS = {11-06 (11G05)},
218
MRNUMBER = {2000m:11002}
219
}
220
221
@article {rohrlich:cyclo,
222
AUTHOR = {Rohrlich, D.\thinspace{}E.},
223
TITLE = {On {$L$}-functions of elliptic curves and cyclotomic towers},
224
JOURNAL = {Invent. Math.},
225
FJOURNAL = {Inventiones Mathematicae},
226
VOLUME = {75},
227
YEAR = {1984},
228
NUMBER = {3},
229
PAGES = {409--423},
230
ISSN = {0020-9910},
231
CODEN = {INVMBH},
232
MRCLASS = {11G40 (11R23 14G10)},
233
MRNUMBER = {86g:11038b},
234
MRREVIEWER = {Karl Rubin}
235
}
236
237
@article{coleman-stein:padicapprox,
238
AUTHOR = {Coleman, R.},
239
TITLE = {Approximation of Infinite-Slope Modular Eigenforms By Finite-Slope Eigenforms},
240
JOURNAL = {To appear in the Dwork Proceedings},
241
YEAR = {2003}
242
}
243
244
@article {stein:index,
245
AUTHOR = {Stein, W.\thinspace{}A.},
246
TITLE = {There are genus one curves over {$\mathbf{Q}$} of every odd index},
247
JOURNAL = {J. Reine Angew. Math.},
248
FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
249
VOLUME = {547},
250
YEAR = {2002},
251
PAGES = {139--147},
252
ISSN = {0075-4102},
253
CODEN = {JRMAA8},
254
MRCLASS = {11G05 (11G18)},
255
MRNUMBER = {2003c:11059},
256
MRREVIEWER = {Imin Chen},
257
}
258
259
@article{dummigan-stein-watkins:motives,
260
AUTHOR = {Dummigan, N. and Watkins, M. and Stein, W.\thinspace{}A.},
261
TITLE = {{Constructing Elements in Shafarevich-Tate Groups of
262
Modular Motives}},
263
JOURNAL = {To appear in ``Number theory and algebraic geometry
264
--- to Peter Swinnerton-Dyer on his 75th birthday'', ed. by
265
Miles Reid and Alexei Skorobogatov}
266
}
267
268
@article{stein:bsdmagma,
269
AUTHOR = {Stein, W.\thinspace{}A.},
270
TITLE = {Studying the {B}irch and {S}winnerton-{D}yer {C}onjecture
271
for {M}odular {A}belian {V}arieties {U}sing {MAGMA}},
272
JOURNAL = {To appear in J.~Cannon, ed., {\em Computational
273
Experiments in Algebra and Geometry}, Springer-Verlag},
274
YEAR = {2003}
275
}
276
277
278
@article {neron,
279
AUTHOR = {N{\'e}ron, A.},
280
TITLE = {Mod\`eles minimaux des vari\'et\'es ab\'eliennes sur les corps
281
locaux et globaux},
282
JOURNAL = {Inst. Hautes \'Etudes Sci. Publ.Math. No.},
283
VOLUME = {21},
284
YEAR = {1964},
285
PAGES = {128},
286
MRCLASS = {14.49 (14.51)},
287
MRNUMBER = {31 \#3423},
288
MRREVIEWER = {M. Artin},
289
}
290
291
@article{conrad-edixhoven-stein:j1p,
292
AUTHOR = {Conrad, B. and Edixhoven, S. and Stein, W.\thinspace{}A.},
293
TITLE = {${J}_1(p)$ {H}as {C}onnected {F}ibers},
294
YEAR = 2003,
295
JOURNAL = {To appear in Documenta Mathematica}
296
}
297
298
@incollection {ribet:abvars,
299
AUTHOR = {Ribet, K.\thinspace{}A.},
300
TITLE = {Abelian varieties over {${\bf Q}$} and modular forms},
301
BOOKTITLE = {Algebra and topology 1992 (Taej\u on)},
302
PAGES = {53--79},
303
PUBLISHER = {Korea Adv. Inst. Sci. Tech.},
304
ADDRESS = {Taej\u on},
305
YEAR = {1992},
306
MRCLASS = {11G18 (11F33 14G35 14H52)},
307
MRNUMBER = {94g:11042},
308
MRREVIEWER = {Bas Edixhoven},
309
}
310
311
@proceedings {MR93k:00030,
312
TITLE = {Algebra and topology 1992},
313
BOOKTITLE = {Proceedings of the Seventh KAIST Mathematics Workshop held in
314
Taej\u on, August 11--14, 1992},
315
EDITOR = {Hahn, S. G. and Suh, D. Y.},
316
PUBLISHER = {Korea Advanced Institute of Science and Technology Mathematics
317
Research Center},
318
ADDRESS = {Taej\u on},
319
YEAR = {1992},
320
PAGES = {x+271},
321
MRCLASS = {00B25},
322
MRNUMBER = {93k:00030},
323
}
324
325
326
327
328
@book {silverman-tate,
329
AUTHOR = {Silverman, J.\thinspace{}H. and Tate, J.},
330
TITLE = {Rational points on elliptic curves},
331
SERIES = {Undergraduate Texts in Mathematics},
332
PUBLISHER = {Springer-Verlag},
333
ADDRESS = {New York},
334
YEAR = {1992},
335
PAGES = {x+281},
336
ISBN = {0-387-97825-9},
337
MRCLASS = {11-01 (11D25 11G05 14H52)},
338
MRNUMBER = {93g:11003},
339
MRREVIEWER = {Andrew Bremner},
340
}
341
342
343
344
345
@article{agashe-stein:manin,
346
author = "Agashe, A. and Stein, W.\thinspace{}A.",
347
title = "The Manin Constant, Congruence Primes, and the Modular Degree",
348
date = 2003,
349
journal = {In progress},
350
}
351
352
@article{agashe-stein:bsd,
353
author = "Agashe, A. and Stein, W.\thinspace{}A.",
354
title = "Visible {E}vidence for the {B}irch and {S}winnerton-{D}yer {C}onjecture
355
for {M}odular {A}belian {V}arieties of {A}nalytic {R}ank~$0$",
356
date = 2003,
357
journal = {To appear in Math. of Computation}
358
}
359
360
@article{agashe-stein:visibility,
361
AUTHOR = {Agashe, A. and Stein, W.\thinspace{}A.},
362
TITLE = {Visibility of {S}hafarevich-{T}ate groups of abelian
363
varieties},
364
JOURNAL = {J. Number Theory},
365
FJOURNAL = {Journal of Number Theory},
366
VOLUME = {97},
367
YEAR = {2002},
368
NUMBER = {1},
369
PAGES = {171--185},
370
ISSN = {0022-314X},
371
CODEN = {JNUTA9},
372
MRCLASS = {11G40 (11G10 14K15)},
373
MRNUMBER = {2003h:11070},
374
MRREVIEWER = {Chandan Singh Dalawat},
375
}
376
377
@article {agashe-stein:schoof-appendix,
378
AUTHOR = {Agashe, A. and Stein, W.\thinspace{}A.},
379
TITLE = {{\em Appendix to {J}oan-{C}. {L}ario and
380
{R}en\'e {S}choof:} {S}ome computations with {H}ecke
381
rings and deformation rings},
382
JOURNAL = {To appear in Exp. Math.}
383
}
384
385
@incollection {birch:EDSAC,
386
AUTHOR = {Birch, B. J.},
387
TITLE = {Conjectures concerning elliptic curves},
388
BOOKTITLE = {Proceedings of Symposia in Pure Mathematics, VIII},
389
PAGES = {106--112},
390
PUBLISHER = {Amer. Math. Soc.},
391
ADDRESS = {Providence, R.I.},
392
YEAR = {1965},
393
MRCLASS = {14.49 (14.40)},
394
MRNUMBER = {30 \#4759},
395
MRREVIEWER = {J. W. S. Cassels},
396
}
397
398
@proceedings {MR82d:10006,
399
TITLE = {Theory of numbers},
400
SERIES = {Proceedings of Symposia in Pure Mathematics},
401
BOOKTITLE = {Proceedings of the Symposium in Pure Mathematics, VIII},
402
EDITOR = {Whiteman, Albert Leon},
403
NOTE = {Corrected reprint of the 1965 original},
404
PUBLISHER = {American Mathematical Society},
405
ADDRESS = {Providence, R.I.},
406
YEAR = {1979},
407
PAGES = {vii+216},
408
ISBN = {0-8218-1408-7},
409
MRCLASS = {10-06},
410
MRNUMBER = {82d:10006},
411
}
412
413
@article{breuil-conrad-diamond-taylor,
414
AUTHOR = {Breuil, C. and Conrad, B. and Diamond, F. and
415
Taylor, R.},
416
TITLE = {On the modularity of elliptic curves over {$\bold Q$}: wild
417
3-adic exercises},
418
JOURNAL = {J. Amer. Math. Soc.},
419
FJOURNAL = {Journal of the American Mathematical Society},
420
VOLUME = {14},
421
YEAR = {2001},
422
NUMBER = {4},
423
PAGES = {843--939 (electronic)},
424
ISSN = {0894-0347},
425
MRCLASS = {11G05 (11F80 11G07 14G35)},
426
MRNUMBER = {2002d:11058},
427
MRREVIEWER = {Karl Rubin},
428
}
429
430
@article {cassels:diophantinecurve,
431
AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
432
TITLE = {Diophantine equations with special reference to elliptic
433
curves},
434
JOURNAL = {J. London Math. Soc.},
435
VOLUME = {41},
436
YEAR = {1966},
437
PAGES = {193--291},
438
}
439
440
@article{CMI:problems,
441
AUTHOR = {Clay Mathematics Institute},
442
TITLE = {Millennium Prize Problems,\hfill\\{\tt http://www.claymath.org/Millennium\_Prize\_Problems/}}
443
}
444
445
@book {neronmodels,
446
AUTHOR = {Bosch, S. and L{\"u}tkebohmert, W. and Raynaud, M.},
447
TITLE = {N\'eron models},
448
PUBLISHER = {Springer-Verlag},
449
ADDRESS = {Berlin},
450
YEAR = {1990},
451
PAGES = {x+325},
452
ISBN = {3-540-50587-3},
453
MRCLASS = {14K15 (11G10 14L15)},
454
MRNUMBER = {91i:14034},
455
MRREVR = {J. Milne},
456
}
457
@article {stein:nonsquaresha,
458
AUTHOR = {Stein, W.\thinspace{}A.},
459
TITLE = {Shafarevich-Tate Groups of Nonsquare Order},
460
PUBLISHER = {Birkh\"auser},
461
journal = {Proceedings of MCAV 2002, Progress of Mathematics (to appear)}
462
}
463
464
@article{stein:phd,
465
author="Stein, W.\thinspace{}A.",
466
title={Explicit approaches to modular abelian varieties},
467
journal = {Ph.D. thesis, University of California, Berkeley},
468
year={2000}
469
}
470
471
@article{atkin-lehner,
472
AUTHOR = {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.},
473
TITLE = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
474
JOURNAL = {Math. Ann.},
475
VOLUME = {185},
476
YEAR = {1970},
477
PAGES = {134--160},
478
}
479
480
481
482
483
%%%%%%%%%%%%%%%% old stuff %%%%%%%%%%%%%%%%%
484
485
486
@article{edixhoven:comparison,
487
AUTHOR = {Edixhoven, B.},
488
TITLE = {Comparison of integral structures on spaces of
489
modular forms of weight two, and computation of spaces of forms
490
mod~$2$ of weight one},
491
DATE = {July, 2003},
492
JOURNAL={preprint}
493
}
494
495
@article {gonzalez-lario:manin,
496
AUTHOR = {Gonz{\'a}lez, J. and Lario, J.-C.},
497
TITLE = {{$\mathbf{Q}$}-curves and their {M}anin ideals},
498
JOURNAL = {Amer. J. Math.},
499
FJOURNAL = {American Journal of Mathematics},
500
VOLUME = {123},
501
YEAR = {2001},
502
NUMBER = {3},
503
PAGES = {475--503},
504
ISSN = {0002-9327},
505
CODEN = {AJMAAN},
506
MRCLASS = {11G05 (11G18)},
507
MRNUMBER = {2002e:11070},
508
MRREVIEWER = {Ivica Gusi{\'c}},
509
}
510
511
@article {stevens:param,
512
AUTHOR = {Stevens, G.},
513
TITLE = {Stickelberger elements and modular parametrizations of
514
elliptic curves},
515
JOURNAL = {Invent. Math.},
516
FJOURNAL = {Inventiones Mathematicae},
517
VOLUME = {98},
518
YEAR = {1989},
519
NUMBER = {1},
520
PAGES = {75--106},
521
ISSN = {0020-9910},
522
CODEN = {INVMBH},
523
MRCLASS = {11G05 (11F11)},
524
MRNUMBER = {90m:11089},
525
MRREVIEWER = {Sheldon Kamienny},
526
}
527
528
@article {pentium,
529
AUTHOR = {Edelman, A.},
530
TITLE = {The mathematics of the {P}entium division bug},
531
JOURNAL = {SIAM Rev.},
532
FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and
533
Applied Mathematics},
534
VOLUME = {39},
535
YEAR = {1997},
536
NUMBER = {1},
537
PAGES = {54--67},
538
ISSN = {0036-1445},
539
CODEN = {SIREAD},
540
MRCLASS = {68M07},
541
MRNUMBER = {98a:68009},
542
MRREVIEWER = {Behrooz Parhami},
543
}
544
545
@book {serre:lie_theory,
546
AUTHOR = {Serre, J-P.},
547
TITLE = {Lie algebras and {L}ie groups},
548
SERIES = {Lecture Notes in Mathematics},
549
VOLUME = {1500},
550
EDITION = {Second},
551
NOTE = {1964 lectures given at Harvard University},
552
PUBLISHER = {Springer-Verlag},
553
ADDRESS = {Berlin},
554
YEAR = {1992},
555
PAGES = {viii+168},
556
ISBN = {3-540-55008-9},
557
MRCLASS = {17-01 (17Bxx 22-01)},
558
MRNUMBER = {93h:17001},
559
}
560
561
562
563
@incollection {ogg:rationalpoints,
564
AUTHOR = {Ogg, A. P.},
565
TITLE = {Rational points on certain elliptic modular curves},
566
BOOKTITLE = {Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV,
567
St. Louis Univ., St. Louis, Mo., 1972)},
568
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569
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570
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572
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573
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574
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575
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577
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578
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579
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580
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582
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594
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595
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596
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600
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604
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605
}
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608
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609
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610
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611
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617
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618
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621
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622
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626
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631
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634
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652
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654
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671
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694
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695
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696
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698
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710
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711
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712
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726
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729
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730
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731
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733
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734
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736
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738
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739
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749
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777
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819
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834
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842
}
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844
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845
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848
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857
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860
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872
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873
AUTHOR = {Schneider, P.},
874
TITLE = {Iwasawa ${L}$-functions of varieties over algebraic number
875
fields. {A} first approach},
876
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877
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878
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881
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899
MRREVIEWER = {T. Ono},
900
}
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903
@incollection {sd:bsd,
904
AUTHOR = {Swinnerton-Dyer, P.},
905
TITLE = {The conjectures of {B}irch and {S}winnerton-{D}yer, and of
906
{T}ate},
907
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PUBLISHER = {Springer},
910
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911
YEAR = {1967},
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MRNUMBER = {37 \#6287},
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MRREVIEWER = {Y. Nakai},
915
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917
@book {MR37:3885,
918
TITLE = {Proceedings of a {C}onference on {L}ocal {F}ields},
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921
YEAR = {1967},
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MRCLASS = {00.04 (12.00)},
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MRNUMBER = {37 \#3885},
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927
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929
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@incollection {rubin:kato,
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AUTHOR = {Rubin, K.},
945
TITLE = {Euler systems and modular elliptic curves},
946
BOOKTITLE = {Galois representations in arithmetic algebraic geometry
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@book {MR2000a:11005,
958
TITLE = {Galois representations in arithmetic algebraic geometry},
959
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961
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971
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981
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983
@article {ribet:endo,
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985
TITLE = {Endomorphisms of semi-stable abelian varieties over number
986
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996
@article{gordon-ono:vis,
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TITLE = {Modular form {C}ongruences and {S}elmer groups},
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JOURNAL = {preprint},
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YEAR = {2002}
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1003
@book {MR2000m:11002,
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1005
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1006
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1007
12--19, 1997,
1008
Edited by C. Viola},
1009
PUBLISHER = {Springer-Verlag},
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1018
@incollection {ribet:torsion,
1019
AUTHOR = {Ribet, K.\thinspace{}A.},
1020
TITLE = {Torsion points on ${J}\sb 0({N})$ and {G}alois
1021
representations},
1022
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1023
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1025
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1026
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MRCLASS = {11G18 (11F80)},
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MRNUMBER = {2001b:11054},
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MRREVIEWER = {Matthew H. Baker},
1030
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1032
1033
@article {merel-stein,
1034
AUTHOR = {Merel, L. and Stein, W.\thinspace{}A.},
1035
TITLE = {The field generated by the points of small prime order on an
1036
elliptic curve},
1037
JOURNAL = {Internat. Math. Res. Notices},
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NUMBER = {20},
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ISSN = {1073-7928},
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MRCLASS = {11G05},
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MRNUMBER = {1 857 596},
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1047
@article {hardy_littlewood:conjf,
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1049
TITLE = {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}.
1050
{O}n the {E}xpression of a {N}umber as a {S}um of {P}rimes.},
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JOURNAL = {Acta. Math.},
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1057
@article {setzer,
1058
AUTHOR = {Setzer, B.},
1059
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1060
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1061
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1062
YEAR = {1975},
1063
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1065
MRNUMBER = {51 \#8121},
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1067
}
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1069
@article {neumann2,
1070
AUTHOR = {Neumann, O.},
1071
TITLE = {Elliptische {K}urven mit vorgeschriebenem
1072
{R}eduktionsverhalten. {I}{I}},
1073
JOURNAL = {Math. Nachr.},
1074
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1075
YEAR = {1973},
1076
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1077
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1079
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1080
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1081
@article {neumann1,
1082
AUTHOR = {Neumann, O.},
1083
TITLE = {Elliptische {K}urven mit vorgeschriebenem
1084
{R}eduktionsverhalten. {I}},
1085
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1087
YEAR = {1971},
1088
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1089
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MRREVIEWER = {J. W. S. Cassels},
1092
}
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1094
@article {stein-watkins:ants5,
1095
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1098
publisher={Springer},
1099
address ={Berlin},
1100
YEAR = {2002}
1101
}
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1104
@incollection {kolyvagin:euler_systems,
1105
AUTHOR = {Kolyvagin, V. A.},
1106
TITLE = {Euler systems},
1107
BOOKTITLE = {The Grothendieck Festschrift, Vol.\ II},
1108
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1109
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1110
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1113
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1114
MRREVIEWER = {Karl Rubin},
1115
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1117
@book {MR92b:00051,
1118
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1119
EDITOR = {Cartier, P. and Illusie, L. and Katz, N. M. and Laumon, G. and
1120
Ribet, K. A.},
1121
NOTE = {A collection of articles written in honor of the 60th birthday
1122
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1123
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@book {stevens:thesis,
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1576
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AUTHOR = {Ramakrishna, R.},
1652
TITLE = {Deforming {G}alois representations and the conjectures
1653
of {S}erre and {F}ontaine-{M}azur},
1654
JOURNAL = {preprint,
1655
\protect{\tt ftp://math.cornell.edu/pub/ravi}},
1656
FJOURNAL = {},
1657
VOLUME = {},
1658
YEAR = {2000},
1659
NUMBER = {},
1660
PAGES = {},
1661
}
1662
1663
@article {ramakrishna:lifting,
1664
AUTHOR = {Ramakrishna, R.},
1665
TITLE = {Lifting {G}alois representations},
1666
JOURNAL = {Invent. Math.},
1667
FJOURNAL = {Inventiones Mathematicae},
1668
VOLUME = {138},
1669
YEAR = {1999},
1670
NUMBER = {3},
1671
PAGES = {537--562},
1672
ISSN = {0020-9910},
1673
CODEN = {INVMBH},
1674
MRCLASS = {11Fxx},
1675
MRNUMBER = {1 719 819},
1676
}
1677
1678
@article {ramakrishna:deform,
1679
AUTHOR = {Ramakrishna, R.},
1680
TITLE = {Deforming an even representation},
1681
JOURNAL = {Invent. Math.},
1682
FJOURNAL = {Inventiones Mathematicae},
1683
VOLUME = {132},
1684
YEAR = {1998},
1685
NUMBER = {3},
1686
PAGES = {563--580},
1687
ISSN = {0020-9910},
1688
CODEN = {INVMBH},
1689
MRCLASS = {11R32 (11R34)},
1690
MRNUMBER = {99h:11128},
1691
MRREVR = {Nigel Boston},
1692
}
1693
1694
1695
@book {haberland,
1696
AUTHOR = {Haberland, Klaus},
1697
TITLE = {Galois cohomology of algebraic number fields},
1698
NOTE = {With two appendices by Helmut Koch and Thomas Zink},
1699
PUBLISHER = {VEB Deutscher Verlag der Wissenschaften},
1700
ADDRESS = {Berlin},
1701
YEAR = {1978},
1702
PAGES = {145},
1703
MRCLASS = {12A60},
1704
MRNUMBER = {81i:12009},
1705
MRREVR = {Chih-Han Sah},
1706
}
1707
1708
1709
1710
@article{dummigan:cp,
1711
author = {Dummigan, N.},
1712
title = {Period ratios of modular forms},
1713
journal= {To appear in Math. Annalen}
1714
}
1715
1716
1717
@article {cohen-oesterle:dimensions,
1718
AUTHOR = {Cohen, H. and Oesterl{\'e}, J.},
1719
TITLE = {Dimensions des espaces de formes modulaires},
1720
BOOKTITLE = {Modular functions of one variable, VI (Proc. Second Internat.
1721
Conf., Univ. Bonn, Bonn, 1976)},
1722
PAGES = {69--78. Lecture Notes in Math., Vol. 627},
1723
PUBLISHER = {Springer},
1724
ADDRESS = {Berlin},
1725
YEAR = {1977},
1726
MRCLASS = {10D15},
1727
MRNUMBER = {57 #12396},
1728
MRREVR = {R. A. Rankin},
1729
}
1730
1731
@book{robert:elliptic,
1732
AUTHOR = {Robert, A.},
1733
TITLE = {Elliptic curves},
1734
NOTE = {Notes from postgraduate lectures given in Lausanne 1971/72,
1735
Lecture Notes in Mathematics, Vol. 326},
1736
PUBLISHER = {Springer-Verlag},
1737
ADDRESS = {Berlin},
1738
YEAR = {1973},
1739
PAGES = {viii+264},
1740
MRCLASS = {14K15},
1741
MRNUMBER = {50 #4594},
1742
MRREVR = {Kuang-yen Shih}
1743
}
1744
1745
@book {dixcohomologie,
1746
TITLE = {Dix expos\'es sur la cohomologie des sch\'emas},
1747
NOTE = {Advanced Studies in Pure Mathematics, Vol. 3},
1748
PUBLISHER = {North-Holland Publishing Co.},
1749
ADDRESS = {Amsterdam},
1750
YEAR = {1968},
1751
PAGES = {vi+386},
1752
MRCLASS = {14.55},
1753
MRNUMBER = {39 #2777},
1754
}
1755
1756
@incollection {grothendieck:brauer3,
1757
AUTHOR = {Grothendieck, Alexander},
1758
TITLE = {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et compl\'ements},
1759
BOOKTITLE = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
1760
PAGES = {88--188},
1761
PUBLISHER = {North-Holland},
1762
ADDRESS = {Amsterdam},
1763
YEAR = {1968},
1764
MRCLASS = {14.55},
1765
MRNUMBER = {39 #5586c},
1766
MRREVR = {J. S. Milne},
1767
}
1768
@incollection {grothendieck:brauer2,
1769
AUTHOR = {Grothendieck, Alexander},
1770
TITLE = {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique},
1771
BOOKTITLE = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
1772
PAGES = {67--87},
1773
PUBLISHER = {North-Holland},
1774
ADDRESS = {Amsterdam},
1775
YEAR = {1968},
1776
MRCLASS = {14.55},
1777
MRNUMBER = {39 #5586b},
1778
}
1779
@incollection {grothendieck:brauer1,
1780
AUTHOR = {Grothendieck, Alexander},
1781
TITLE = {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et
1782
interpr\'etations diverses},
1783
BOOKTITLE = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
1784
PAGES = {46--66},
1785
PUBLISHER = {North-Holland},
1786
ADDRESS = {Amsterdam},
1787
YEAR = {1968},
1788
MRCLASS = {14.55},
1789
MRNUMBER = {39 #5586a},
1790
}
1791
1792
@book {eisenbud-harris-2,
1793
AUTHOR = {Eisenbud, D. and Harris, J.},
1794
TITLE = {{S}chemes, {T}he language of modern algebraic geometry},
1795
NOTE = {Graduate Texts in Mathematics, Vol.\ 197},
1796
PUBLISHER = {Springer-Verlag},
1797
ADDRESS = {Berlin},
1798
YEAR = {},
1799
PAGES = {}
1800
}
1801
1802
@book {eisenbud-harris,
1803
AUTHOR = {Eisenbud, D. and Harris, J.},
1804
TITLE = {{S}chemes, {T}he language of modern algebraic geometry},
1805
PUBLISHER = {Wadsworth \& Brooks/Cole Advanced Books \& Software},
1806
ADDRESS = {Pacific Grove, CA},
1807
YEAR = {1992},
1808
PAGES = {xii+157},
1809
ISBN = {0-534-17606-2; 0-534-17604-6},
1810
MRCLASS = {14-01 (14A15)},
1811
MRNUMBER = {93k:14001},
1812
MRREVR = {Alexey N. Rudakov},
1813
}
1814
1815
1816
1817
@article {coleman:serre,
1818
AUTHOR = {Coleman, R.\thinspace{}F.},
1819
TITLE = {Serre's conjecture: {T}he {J}ugentraum of the 20th century},
1820
NOTE = {XII School of Algebra, Part I (Portuguese) (Diamantina, 1992)},
1821
JOURNAL = {Mat. Contemp.},
1822
FJOURNAL = {Matem\'atica Contempor\cflex anea},
1823
VOLUME = {6},
1824
YEAR = {1994},
1825
PAGES = {13--18},
1826
ISSN = {0103-9059},
1827
MRCLASS = {12F05 (11F03 12F12)},
1828
MRNUMBER = {95j:12003},
1829
MRREVR = {Henri Darmon},
1830
}
1831
1832
@article {edixhoven:erratum,
1833
AUTHOR = {Edixhoven, B.},
1834
TITLE = {Erratum and addendum: ``{T}he role of {S}erre's conjecture in
1835
the proof of {F}ermat's theorem''},
1836
JOURNAL = {Gaz. Math.},
1837
FJOURNAL = {Gazette des Math\'ematiciens},
1838
NUMBER = {67},
1839
YEAR = {1996},
1840
PAGES = {19},
1841
ISSN = {0224-8999},
1842
MRCLASS = {11F33 (11D41 11F80 11G05)},
1843
MRNUMBER = {96k:11055b},
1844
MRREVR = {Fernando Q. Gouv\^ea},
1845
}
1846
1847
@article {edixhoven:serrerole,
1848
AUTHOR = {Edixhoven, B.},
1849
TITLE = {Le r\^{o}le de la conjecture de {S}erre dans la
1850
d\'emonstration du th\'eor\`eme de {F}ermat},
1851
JOURNAL = {Gaz. Math.},
1852
FJOURNAL = {Gazette des Math\'ematiciens},
1853
NUMBER = {66},
1854
YEAR = {1995},
1855
PAGES = {25--41},
1856
ISSN = {0224-8999},
1857
MRCLASS = {11F33 (11D41 11F80 11G05)},
1858
MRNUMBER = {96k:11055a},
1859
MRREVR = {Fernando Q. Gouv\^ea},
1860
}
1861
1862
1863
@article {gouvea-mazur:families,
1864
AUTHOR = {Gouv\^ea, F. and Mazur, B.},
1865
TITLE = {Families of modular eigenforms},
1866
JOURNAL = {Math. Comp.},
1867
FJOURNAL = {Mathematics of Computation},
1868
VOLUME = {58},
1869
YEAR = {1992},
1870
NUMBER = {198},
1871
PAGES = {793--805},
1872
ISSN = {0025-5718},
1873
CODEN = {MCMPAF},
1874
MRCLASS = {11F33 (11Y35 14G20)},
1875
MRNUMBER = {93d:11049},
1876
MRREVR = {Bas Edixhoven}
1877
}
1878
1879
@incollection {eigencurve,
1880
AUTHOR = {Coleman, R. and Mazur, B.},
1881
TITLE = {The {E}igencurve},
1882
BOOKTITLE = {Galois representations in arithmetic algebraic geometry
1883
(Durham, 1996)},
1884
PAGES = {1--113},
1885
PUBLISHER = {Cambridge Univ. Press},
1886
ADDRESS = {Cambridge},
1887
YEAR = {1998},
1888
MRCLASS = {11Fxx (11Gxx)},
1889
MRNUMBER = {1 696 469}
1890
}
1891
1892
1893
1894
@book {eisenbud,
1895
AUTHOR = {Eisenbud, D.},
1896
TITLE = {Commutative Algebra with a View Toward Algebraic Geometry},
1897
PUBLISHER = {Springer-Verlag},
1898
ADDRESS = {New York},
1899
YEAR = {1995},
1900
PAGES = {xvi+785},
1901
ISBN = {0-387-94268-8; 0-387-94269-6},
1902
MRCLASS = {13-01 (14A05)},
1903
MRNUMBER = {97a:13001},
1904
MRREVR = {Matthew Miller},
1905
}
1906
1907
@book {cassels-flynn,
1908
AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.
1909
and Flynn, E.\thinspace{}V.},
1910
TITLE = {Prolegomena to a middlebrow arithmetic of curves
1911
of genus \protect{$2$}},
1912
PUBLISHER = {Cambridge University Press},
1913
ADDRESS = {Cambridge},
1914
YEAR = {1996},
1915
PAGES = {xiv+219},
1916
ISBN = {0-521-48370-0},
1917
MRCLASS = {11G30 (11Y50 14G25)},
1918
MRNUMBER = {97i:11071},
1919
MRREVR = {Joseph H. Silverman},
1920
}
1921
1922
1923
1924
@article {hida:iwasawa,
1925
AUTHOR = {Hida, H.},
1926
TITLE = {Iwasawa modules attached to congruences of cusp forms},
1927
JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
1928
FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
1929
Quatri\`eme S\'erie},
1930
VOLUME = {19},
1931
YEAR = {1986},
1932
NUMBER = {2},
1933
PAGES = {231--273},
1934
ISSN = {0012-9593},
1935
CODEN = {ASENAH},
1936
MRCLASS = {11F33 (11G18 11R23)},
1937
MRNUMBER = {88i:11023},
1938
MRREVR = {Yasutaka Ihara},
1939
}
1940
1941
1942
1943
@article {hida:invent86,
1944
AUTHOR = {Hida, H.},
1945
TITLE = {Galois representations into
1946
\protect{${\rm {G}{L}}\sb 2({\bf {Z}}\sb
1947
p[[{X}]])$} attached to ordinary cusp forms},
1948
JOURNAL = {Invent. Math.},
1949
FJOURNAL = {Inventiones Mathematicae},
1950
VOLUME = {85},
1951
YEAR = {1986},
1952
NUMBER = {3},
1953
PAGES = {545--613},
1954
ISSN = {0020-9910},
1955
CODEN = {INVMBH},
1956
MRCLASS = {11F11 (11F33 11F85 11R23)},
1957
MRNUMBER = {87k:11049},
1958
MRREVR = {Ernst-Wilhelm Zink},
1959
}
1960
1961
1962
@incollection {elkies:heegner,
1963
AUTHOR = {Elkies, N.\thinspace{}D.},
1964
TITLE = {Heegner point computations},
1965
BOOKTITLE = {Algorithmic number theory (Ithaca, NY, 1994)},
1966
PAGES = {122--133},
1967
PUBLISHER = {Springer},
1968
ADDRESS = {Berlin},
1969
YEAR = {1994},
1970
}
1971
@article {scholl:motivesinvent,
1972
AUTHOR = {Scholl, A.\thinspace{}J.},
1973
TITLE = {Motives for modular forms},
1974
JOURNAL = {Invent. Math.},
1975
FJOURNAL = {Inventiones Mathematicae},
1976
VOLUME = {100},
1977
YEAR = {1990},
1978
NUMBER = {2},
1979
PAGES = {419--430},
1980
ISSN = {0020-9910},
1981
CODEN = {INVMBH},
1982
}
1983
@incollection {scholl:kato,
1984
author = {Scholl, A.\thinspace{}J.},
1985
title = {An introduction to {K}ato's {E}uler systems},
1986
booktitle = {Galois Representations in Arithmetic Algebraic Geometry},
1987
pages = {379--460},
1988
year = {1998},
1989
publisher = {Cambridge University Press}
1990
}
1991
1992
@proceedings {lms254,
1993
title = {Galois Representations in Arithmetic Algebraic Geometry},
1994
booktitle = {Galois Representations in Arithmetic Algebraic Geometry},
1995
editor = {Scholl A.\thinspace{}J. and Taylor R.\thinspace{}L.},
1996
pages = {493},
1997
year = {1998},
1998
publisher = {Cambridge University Press}
1999
}
2000
2001
%qa1.h3
2002
@article{artin:conjecture,
2003
author = {Artin, E.},
2004
title = {{\"U}ber eine neue {A}rt von {L}-Reihen},
2005
journal={Abh. Math. Sem. Univ. Hamburg},
2006
volume ={3},
2007
year ={1923 or 1924??? CHECK!},
2008
pages ={89--108}
2009
}
2010
2011
@article{artin:conjecture2,
2012
author = {Artin, E},
2013
title = {Zur {T}heorie der {L}-{R}eihen mit allgemeinen
2014
{G}ruppencharakteren},
2015
journal={Abh. math. Semin. Univ. Hamburg},
2016
volume ={8},
2017
year ={1930},
2018
pages ={292--306}
2019
}
2020
2021
@article{buzzard-stein:artin,
2022
AUTHOR = {Buzzard, K. and Stein, W.\thinspace{}A.},
2023
TITLE = {A mod five approach to modularity of icosahedral {G}alois
2024
representations},
2025
JOURNAL = {Pacific J. Math.},
2026
FJOURNAL = {Pacific Journal of Mathematics},
2027
VOLUME = {203},
2028
YEAR = {2002},
2029
NUMBER = {2},
2030
PAGES = {265--282},
2031
ISSN = {0030-8730},
2032
CODEN = {PJMAAI},
2033
MRCLASS = {11F80},
2034
MRNUMBER = {2003c:11052},
2035
MRREVIEWER = {Mark Edward Tristan Dickinson},
2036
}
2037
2038
@proceedings {MR98g:11001,
2039
TITLE = {Computational perspectives on number theory},
2040
BOOKTITLE = {Proceedings of the conference in honor of A. O. L. Atkin held
2041
at the University of Illinois, Chicago, IL, September 1995},
2042
EDITOR = {Buell, D. A. and Teitelbaum, J. T.},
2043
PUBLISHER = {American Mathematical Society},
2044
ADDRESS = {Providence, RI},
2045
YEAR = {1998},
2046
PAGES = {x+232},
2047
ISBN = {0-8218-0880-X},
2048
}
2049
2050
2051
@proceedings {MR95j:11119,
2052
TITLE = {Algorithmic number theory},
2053
BOOKTITLE = {Proceedings of the First International Symposium (ANTS-I) held
2054
at Cornell University, Ithaca, New York, May 6--9, 1994},
2055
EDITOR = {Adleman, Leonard M. and Huang, Ming-Deh},
2056
PUBLISHER = {Springer-Verlag},
2057
ADDRESS = {Berlin},
2058
YEAR = {1994},
2059
PAGES = {x+323},
2060
ISBN = {3-540-58691-1},
2061
}
2062
2063
2064
2065
@incollection {elkies:ffield,
2066
AUTHOR = {Elkies, N.\thinspace{}D.},
2067
TITLE = {Elliptic and modular curves over finite fields and related
2068
computational issues},
2069
BOOKTITLE = {Computational perspectives on number theory (Chicago, IL,
2070
1995)},
2071
PAGES = {21--76},
2072
PUBLISHER = {Amer. Math. Soc.},
2073
ADDRESS = {Providence, RI},
2074
YEAR = {1998},
2075
}
2076
2077
2078
2079
@article {jones:thesis,
2080
author = {Jones, D.\thinspace{}M.},
2081
title = {On modular {G}alois representations in characteristic $3$},
2082
year = {1998},
2083
journal = {U.\thinspace{}C. Berkeley Ph.D. thesis}
2084
}
2085
2086
2087
2088
@article {stein:vismordell,
2089
AUTHOR = {Stein, W.\thinspace{}A.},
2090
TITLE = {{V}isualizing {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves {U}sing
2091
{S}hafarevich-{T}ate {G}roups},
2092
YEAR = {2002},
2093
journal = {In preparation}
2094
}
2095
2096
2097
@article {ash-stevens,
2098
AUTHOR = {Ash, A. and Stevens, G.},
2099
TITLE = {Cohomology of arithmetic groups and congruences between systems
2100
of {H}ecke eigenvalues},
2101
JOURNAL = {J. Reine Angew. Math.},
2102
FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
2103
VOLUME = {365},
2104
YEAR = {1986},
2105
PAGES = {192--220},
2106
ISSN = {0075-4102},
2107
CODEN = {JRMAA8},
2108
}
2109
2110
@article {buzzard:level,
2111
author = {Buzzard, K.},
2112
title = {On level-lowering for mod 2 representations},
2113
journal= {preprint}
2114
}
2115
2116
2117
@article {RAMA,
2118
author = {Ramakrishna, R.},
2119
title = {Lifting {G}alois representations},
2120
journal = {preprint}
2121
}
2122
2123
@article {SBTAYLOR,
2124
AUTHOR = {Shepherd-Barron, N. I. and Taylor, R.},
2125
TITLE = {Mod 2 and mod 5 icosahedral representations},
2126
JOURNAL = {J. Amer. Math. Soc.},
2127
FJOURNAL = {Journal of the American Mathematical Society},
2128
VOLUME = {10},
2129
YEAR = {1997},
2130
NUMBER = {2},
2131
PAGES = {283--298},
2132
ISSN = {0894-0347},
2133
}
2134
2135
@article {DOUD,
2136
AUTHOR = {Doud, D.},
2137
TITLE = {\protect{${S}\sb 4$} and \protect{$\tilde {S}{}\sb 4$}
2138
extensions of \protect{${\bf {Q}}$}
2139
ramified at only one prime},
2140
JOURNAL = {J. Number Theory},
2141
FJOURNAL = {Journal of Number Theory},
2142
VOLUME = {75},
2143
YEAR = {1999},
2144
NUMBER = {2},
2145
PAGES = {185--197},
2146
ISSN = {0022-314X},
2147
CODEN = {JNUTA9},
2148
}
2149
2150
2151
@proceedings {MR90b:11003,
2152
TITLE = {Number theory},
2153
BOOKTITLE = {Proceedings of the Fifteenth Journ\'ees Arithm\'etiques held at
2154
the University of Ulm, Ulm, September 14--18, 1987},
2155
EDITOR = {Schlickewei, H. P. and Wirsing, E.},
2156
PUBLISHER = {Springer-Verlag},
2157
ADDRESS = {New York},
2158
YEAR = {1989},
2159
PAGES = {vi+266},
2160
ISBN = {0-387-51397-3},
2161
}
2162
2163
@incollection {FREYTWO,
2164
AUTHOR = {Frey, G.},
2165
TITLE = {Links between solutions of
2166
\protect{${A}-{B}={C}$} and elliptic curves},
2167
BOOKTITLE = {Number theory (Ulm, 1987)},
2168
PAGES = {31--62},
2169
PUBLISHER = {Springer},
2170
ADDRESS = {New York},
2171
YEAR = {1989},
2172
}
2173
@article {FREYONE,
2174
AUTHOR = {Frey, G.},
2175
TITLE = {Links between stable elliptic curves and
2176
certain {D}iophantine \protect{\nobreak{equations}}},
2177
JOURNAL = {Ann. Univ. Sarav. Ser. Math.},
2178
FJOURNAL = {Annales Universitatis Saraviensis. Series Mathematicae},
2179
VOLUME = {1},
2180
YEAR = {1986},
2181
NUMBER = {1},
2182
PAGES = {iv+40},
2183
}
2184
2185
2186
@article {fujiwara,
2187
author = {Fujiwara, K.},
2188
title = {Level optimization in the totally real case},
2189
journal= {in preparation},
2190
year = {1999}
2191
}
2192
2193
@article {jarvis:mazur,
2194
AUTHOR = {Jarvis, F.},
2195
TITLE = {Mazur's principle for totally real fields of odd degree},
2196
JOURNAL = {Compositio Math.},
2197
FJOURNAL = {Compositio Mathematica},
2198
VOLUME = {116},
2199
YEAR = {1999},
2200
NUMBER = {1},
2201
PAGES = {39--79},
2202
ISSN = {0010-437X},
2203
CODEN = {CMPMAF},
2204
}
2205
@article {jarvis:level,
2206
AUTHOR = {Jarvis, F.},
2207
TITLE = {Level lowering for modular mod \protect{$\ell$}
2208
representations over totally real fields\-},
2209
JOURNAL = {Math. Ann.},
2210
FJOURNAL = {Mathematische Annalen},
2211
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2220
TITLE = {On \protect{G}alois representations
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TITLE = {\protect{${L}$}-functions and
2276
\protect{T}amagawa numbers of motives},
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YEAR = {1990},
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2287
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2301
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@incollection{birch:bsd,
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AUTHOR = {Birch, B.\thinspace{}J.},
2313
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2314
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2320
}
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@incollection {birch:hecke_actions,
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2324
TITLE = {Hecke actions on classes of ternary quadratic forms},
2325
BOOKTITLE = {Computational number theory (Debrecen, 1989)},
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MRNUMBER = {93i:11047},
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}
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2335
@proceedings {MR92i:11131,
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2339
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2341
PUBLISHER = {Walter de Gruyter \& Co.},
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MRCLASS = {11Yxx (11-06)},
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MRNUMBER = {92i:11131},
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}
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2350
@article {boston-lenstra-ribet,
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AUTHOR = {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.}
2352
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2353
TITLE = {Quotients of group rings arising from two-dimensional
2354
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2355
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CODEN = {CASMEI},
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}
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2366
@book{buhler:thesis,
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2375
}
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@article{galbraith,
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2379
title = {Equations for modular curves},
2380
Year = {1996},
2381
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2382
pages = {91 pp.}
2383
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@article{BRUE,
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2388
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2389
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volume = {75},
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@article{brumer:rank,
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2397
TITLE = {The rank of \protect{${J}\sb 0({N})$}},
2398
NOTE = {Columbia University Number Theory Seminar (New York, 1992)},
2399
JOURNAL = {Ast\'erisque},
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@article {cassels:arithmeticIV,
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AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
2409
TITLE = {Arithmetic on curves of genus \protect{$1$}. {I}{V}.
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@article {cassels:arithmeticV,
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AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
2419
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2420
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2429
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2430
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2431
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YEAR = {1967},
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@article{CAREARLY,
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author="Carayol, H.",
2440
title={Sur les \protect{repr\'esentations}
2441
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journal={Ann. scient. \protect{\'Ec.} Norm. Sup.,
2444
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2445
volume={19},
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year={1986},
2447
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2450
@article{carayol:modell,
2451
author={Carayol, H.},
2452
title={Sur les \protect{repr\'esentations} galoisiennes
2453
modulo \protect{$\ell$ attach\'ees} aux formes modulaires},
2454
journal={Duke Math. J.},
2455
volume={59},
2456
year ={1989},
2457
pages ={785--801}
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2463
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@article{cremona:onlinetables,
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2475
@article{womack:ranktable,
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2479
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@book{cremona:algs,
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2485
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2486
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2490
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2493
@article {cremona:periods,
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@article {gouvea:ordinary,
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ISSN = {0022-314X},
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CODEN = {JNUTA9},
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2519
@article{cremona:gammaone,
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AUTHOR = {Cremona, J.\thinspace{}E.},
2521
TITLE = {Modular symbols for \protect{$\Gamma\sb 1({N})$}
2522
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2534
2535
@article {cremona-mazur,
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2537
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@book {curtis-reiner,
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2551
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2556
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}
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@incollection {darmon:serre,
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2562
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2563
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2568
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2570
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2571
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@incollection{ddt,
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2575
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2576
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YEAR = {1994},
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}
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@article{eichler:quadratic,
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2592
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volume = {43},
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year = {1937},
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@book {knapp:elliptic,
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@article {lang-tate,
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@article{shimizu:zeta,
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author = {Shimizu, H.},
2623
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2624
JOURNAL = {Ann. of Math. (2)},
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PAGES = {166--193},
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@inproceedings {deligne-rapoport,
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}
2641
2642
@article {serre:enseign,
2643
AUTHOR = {Serre, J-P.},
2644
TITLE = {Divisibilit\'e de certaines fonctions arithm\'etiques},
2645
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2646
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YEAR = {1976},
2648
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2649
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MRNUMBER = {55 #7958},
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2653
}
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2655
@inproceedings {serre:antwerp72,
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AUTHOR = {Serre, J-P.},
2657
TITLE = {Formes modulaires et fonctions z\^eta $p$-adiques},
2658
BOOKTITLE = {Proceedings of the International Summer School, University of
2659
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PAGES = {191--268. Lecture Notes in Math., Vol. 350},
2661
PUBLISHER = {Springer},
2662
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2663
YEAR = {1973},
2664
MRCLASS = {10D05},
2665
MRNUMBER = {53 #7949a},
2666
MRREVR = {K.-B. Gundlach},
2667
}
2668
2669
2670
@book {MR48:2080,
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TITLE = {Modular functions of one variable. {I}{I}{I}},
2672
BOOKTITLE = {Proceedings of the International Summer School, University of
2673
Antwerp, RUCA, July 17--August 3, 1972},
2674
EDITOR = {Kuyk, Willem and Serre, J.-P.},
2675
NOTE = {Lecture Notes in Mathematics, Vol. 350},
2676
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2677
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2678
YEAR = {1973},
2679
PAGES = {iv+350},
2680
MRCLASS = {10D05 (14K22)},
2681
MRNUMBER = {48 #2080},
2682
}
2683
2684
% MR52:284,
2685
@article {deligne-serre,
2686
AUTHOR = {Deligne, P. and Serre, J-P.},
2687
TITLE = {Formes modulaires de poids $1$},
2688
JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
2689
VOLUME = {7},
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YEAR = {1974},
2691
PAGES = {507--530 (1975)},
2692
}
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2694
@article {diamond-kramer,
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AUTHOR = {Diamond, F. and Kramer, K.},
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@article{hijikata:trace,
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author={Hijikata, H.},
2708
title={Explicit formula of the traces
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2710
\protect{$\Gamma_0(N)$}},
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journal={J. Math. Soc. Japan},
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number={1},
2713
volume={26},
2714
year={1974},
2715
pages={56--82}
2716
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2717
2718
@book {katzmazur,
2719
AUTHOR = {Katz, N.\thinspace{}M. and Mazur, B.},
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TITLE = {Arithmetic moduli of elliptic curves},
2721
PUBLISHER = {Princeton University Press},
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YEAR = {1985},
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PAGES = {xiv+514},
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ISBN = {0-691-08349-5, 0-691-08352-5},
2726
}
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@incollection {lenstra-smit:explicit,
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AUTHOR = {de Smit, B. and Lenstra, H.\thinspace{}W.,Jr.},
2731
TITLE = {Explicit construction of universal deformation rings},
2732
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YEAR = {1997},
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}
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@article {livne:conductors,
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AUTHOR = {Livn{\'e}, R.},
2742
TITLE = {On the conductors of mod \protect{$\ell$}
2743
\protect{G}alois representations coming
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JOURNAL = {J. Number Theory},
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FJOURNAL = {Journal of Number Theory},
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VOLUME = {31},
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2749
NUMBER = {2},
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ISSN = {0022-314X},
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CODEN = {JNUTA9},
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}
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2755
@incollection {mazur:deforming,
2756
AUTHOR = {Mazur, B.},
2757
TITLE = {Deforming \protect{G}alois representations},
2758
BOOKTITLE = {Galois groups over \protect{${\bf Q}$} (Berkeley, CA, 1987)},
2759
PAGES = {385--437},
2760
PUBLISHER = {Springer},
2761
ADDRESS = {New York},
2762
YEAR = {1989},
2763
}
2764
2765
@article {mazur-ribet,
2766
AUTHOR = {Mazur, B. and Ribet, K.\thinspace{}A.},
2767
TITLE = {Two-dimensional representations in the arithmetic of modular
2768
curves},
2769
NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
2770
JOURNAL = {Ast\'erisque},
2771
FJOURNAL = {Ast\'erisque},
2772
NUMBER = {196-197},
2773
YEAR = {1991},
2774
PAGES = {6, 215--255 (1992)},
2775
ISSN = {0303-1179},
2776
}
2777
2778
@article {ono:partition,
2779
AUTHOR = {Ono, K. and Guo, L.},
2780
TITLE = {The partition function and the arithmetic of certain
2781
modular \protect{$L$}-functions},
2782
JOURNAL = {International Mathematical Research Notes},
2783
NUMBER = {},
2784
YEAR = {1999},
2785
PAGES = {},
2786
}
2787
2788
@book {MR89b:14029,
2789
TITLE = {Arithmetic geometry},
2790
EDITOR = {Cornell, G. and Silverman, J.\thinspace{}H.},
2791
NOTE = {Papers from the conference held at the University of
2792
Connecticut, Storrs, Conn., July 30--August 10, 1984},
2793
PUBLISHER = {Springer-Verlag},
2794
ADDRESS = {New York},
2795
YEAR = {1986},
2796
PAGES = {xvi+353},
2797
ISBN = {0-387-96311-1},
2798
}
2799
2800
@book{milne:duality,
2801
author = {Milne, J.\thinspace{}S.},
2802
TITLE = {Arithmetic duality theorems},
2803
PUBLISHER = {Academic Press Inc.},
2804
ADDRESS = {Boston, Mass.},
2805
YEAR = {1986},
2806
PAGES = {x+421},
2807
ISBN = {0-12-498040-6},
2808
}
2809
2810
@book {milne:etale,
2811
AUTHOR = {Milne, J.\thinspace{}S.},
2812
TITLE = {\'{E}tale cohomology},
2813
PUBLISHER = {Princeton University Press},
2814
ADDRESS = {Princeton, N.J.},
2815
YEAR = {1980},
2816
PAGES = {xiii+323},
2817
ISBN = {0-691-08238-3},
2818
MRCLASS = {14-02 (14F20 18F99)},
2819
MRNUMBER = {81j:14002},