The web of modularity: arithmetic of the coefficients of modular forms and q-series
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2004
|
| Schriftenreihe: | Regional conference series in mathematics
102 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index Includes bibliographical references and index |
| Beschreibung: | VIII, 216 |
| ISBN: | 0821833685 |
Internformat
MARC
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| 100 | 1 | |a Ono, Ken |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The web of modularity |b arithmetic of the coefficients of modular forms and q-series |c Ken Ono |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2004 | |
| 300 | |a VIII, 216 | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Regional conference series in mathematics |v 102 | |
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Formes modulaires | |
| 650 | 4 | |a Séries Q | |
| 650 | 4 | |a Forms, Modular | |
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Datensatz im Suchindex
| _version_ | 1804130408167636992 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1. Basic facts 1
1.1. Congruence subgroups 1
1.2. Integer weight modular forms 3
1.3. Half integral weight modular forms 10
1.4. Dedekind s eta function 16
Chapter 2. Integer weight modular forms 21
2.1. Hecke operators 21
2.2. Twists of modular forms 22
2.3. The Theta operator 23
2.4. Further operators 27
2.5. Newforms 28
2.6. Divisors of modular forms on SL2(Z) 31
2.7. Modular forms modulo 2 on SL2(Z) 32
2.8. Modular forms modulo p on SL2(Z) for p 5 35
2.9. Sturm s Theorem 40
2.10. Theory of Serre and Swinnerton Dyer 41
2.11. [/(p) congruences for weakly holomorphic modular forms 43
Chapter 3. Half integral weight modular forms 49
3.1. Hecke operators 49
3.2. Further operators 50
3.3. Shimura s correspondence 52
3.4. Kohnen s theory 54
3.5. Congruences for coefficients of half integral weight forms 56
3.6. Nonvanishing of Fourier coefficients 61
3.7. Open problems 68
Chapter 4. Product expansions of modular forms on SL2CZ) 69
4.1. Introduction 69
4.2. Borcherds products 69
4.3. A sequence of weight 3/2 modular forms 72
4.4. p adic properties of infinite product exponents 74
4.5. Polynomial recursions and infinite products of forms on SL2(Z) 80
4.6. Open problems 83
Chapter 5. Partitions 85
5.1. Introduction 85
5.2. Congruences for p(n) 89
vi CONTENTS
5.3. Distribution of p(n) modulo M 101
5.4. Open problems 106
Chapter 6. Weierstrass points on modular curves 109
6.1. Introduction 109
6.2. Weierstrass points and supersingular points 110
6.3. The X0(p) cases 112
6.4. Open problems 118
Chapter 7. Traces of singular moduli and class equations 121
7.1. Introduction 121
7.2. A result of Gross and Zagier 121
7.3. Formulas for traces and Hecke traces of singular moduli 123
7.4. p adic properties of traces of singular moduli 125
7.5. t/(p) congruences for class equations 130
7.6. Open problems 132
Chapter 8. Class numbers of quadratic fields 133
8.1. Introduction 133
8.2. Class numbers as coefficients of modular forms 134
8.3. Indivisibility of class numbers of imaginary quadratic fields 136
8.4. Indivisibility of class numbers of real quadratic fields 138
8.5. Divisibility of class numbers 143
8.6. Open problems 146
Chapter 9. Central values of modular L functions and applications 149
9.1. Introduction 149
9.2. Central critical values of modular ./[/ functions 149
9.3. Coefficients of half integral weight modular forms 153
9.4. Nonvanishing results 155
9.5. Elements in Selmer and Shafarevich Tate groups 157
9.6. Open problems 161
Chapter 10. Basic hypergeometric generating functions for L values 165
10.1. Introduction 165
10.2. Basic hypergeometric series 165
10.3. Summing the tails of certain infinite products 168
10.4. Generating functions for Z values 175
10.5. Open problems 182
Chapter 11. Gaussian hypergeometric functions 183
11.1. Definitions and notation 183
11.2. Arithmetic of certain special values 186
11.3. Traces of Hecke operators 196
11.4. Beukers supercongruence for Apery numbers 198
11.5. Further congruences 203
11.6. Open problems 204
Bibliography 207
Index 215
|
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| discipline | Mathematik |
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| id | DE-604.BV017667190 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:20:33Z |
| institution | BVB |
| isbn | 0821833685 |
| language | English |
| lccn | 2003063710 |
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| physical | VIII, 216 |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Ono, Ken Verfasser aut The web of modularity arithmetic of the coefficients of modular forms and q-series Ken Ono Providence, R.I. American Mathematical Society 2004 VIII, 216 txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 102 Includes bibliographical references and index Formes modulaires Séries Q Forms, Modular q-series Modulform (DE-588)4128299-1 gnd rswk-swf q-Reihe (DE-588)4227281-6 gnd rswk-swf Modulform (DE-588)4128299-1 s q-Reihe (DE-588)4227281-6 s DE-604 Regional conference series in mathematics 102 (DE-604)BV000004346 102 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010624666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ono, Ken The web of modularity arithmetic of the coefficients of modular forms and q-series Regional conference series in mathematics Formes modulaires Séries Q Forms, Modular q-series Modulform (DE-588)4128299-1 gnd q-Reihe (DE-588)4227281-6 gnd |
| subject_GND | (DE-588)4128299-1 (DE-588)4227281-6 |
| title | The web of modularity arithmetic of the coefficients of modular forms and q-series |
| title_auth | The web of modularity arithmetic of the coefficients of modular forms and q-series |
| title_exact_search | The web of modularity arithmetic of the coefficients of modular forms and q-series |
| title_full | The web of modularity arithmetic of the coefficients of modular forms and q-series Ken Ono |
| title_fullStr | The web of modularity arithmetic of the coefficients of modular forms and q-series Ken Ono |
| title_full_unstemmed | The web of modularity arithmetic of the coefficients of modular forms and q-series Ken Ono |
| title_short | The web of modularity |
| title_sort | the web of modularity arithmetic of the coefficients of modular forms and q series |
| title_sub | arithmetic of the coefficients of modular forms and q-series |
| topic | Formes modulaires Séries Q Forms, Modular q-series Modulform (DE-588)4128299-1 gnd q-Reihe (DE-588)4227281-6 gnd |
| topic_facet | Formes modulaires Séries Q Forms, Modular q-series Modulform q-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010624666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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