Topics in classical automorphic forms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1997
|
| Schriftenreihe: | Graduate studies in mathematics
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 259 S. graph. Darst. |
| ISBN: | 0821807773 9780821807774 |
Internformat
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| 245 | 1 | 0 | |a Topics in classical automorphic forms |c Henryk Iwaniec |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1997 | |
| 300 | |a XII, 259 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 17 | |
| 650 | 4 | |a Formes automorphes | |
| 650 | 7 | |a Formes automorphes |2 ram | |
| 650 | 4 | |a Automorphic forms | |
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Datensatz im Suchindex
| _version_ | 1804126831194931200 |
|---|---|
| adam_text | Contents
Preface xi
Chapter 0. Introduction 1
Chapter 1. The Classical Modular Forms 3
1.1. Periodic functions 3
1.2. Elliptic functions 6
1.3. Modular functions 10
1.4. The Fourier expansion of Eisenstein series 13
1.5. The modular group 15
1.6. The linear space of modular forms 18
Chapter 2. Automorphic Forms in General 23
2.1. The hyperbolic plane 23
2.2. The classification of motions 27
2.3. Discrete groups — Fuchsian groups 29
2.4. Congruence groups 34
2.5. Double coset decomposition 37
2.6. Multiplier systems 40
2.7. Automorphic forms 42
2.8. The eta function and the theta function 44
vii
viii Contents
Chapter 3. The Eisenstein and the Poincare Series 47
3.1. General Poincare series 47
3.2. Fourier expansion of Poincare series 49
3.3. The Hilbert space of cusp forms 52
Chapter 4. Kloosterman Sums 57
4.1. General Kloosterman sums 57
4.2. Kloosterman sums for congruence groups 58
4.3. The classical Kloosterman sums 59
4.4. Power moments of Kloosterman sums 61
4.5. Sums of Kloosterman sums 65
4.6. The Salie sums 66
Chapter 5. Bounds for the Fourier Coefficients of Cusp Forms 69
5.1. General estimates 69
5.2. Estimates by Kloosterman sums 72
5.3. Coefficients of cusp forms with theta multiplier 75
5.4. Linear forms in Fourier coefficients of cusp forms 81
5.5. Spectral analysis of the diagonal symbol 83
Chapter 6. Hecke Operators 91
6.1. Introduction 91
6.2. Hecke operators Tn 92
6.3. The Hecke operators on periodic functions 94
6.4. The Hecke operators for the modular group 98
6.5. The Hecke operators with a character 101
6.6. An overview of newforms 107
6.7. Hecke eigencuspforms for a primitive character 108
6.8. Final remarks 118
Chapter 7. Automorphic L functions 119
7.1. Introduction 119
7.2. The Hecke L functions 120
7.3. Twisting automorphic forms and L functions 124
7.4. Converse theorems 126
Contents ix
Chapter 8. Cusp Forms Associated with Elliptic Curves 133
8.1. The Hasse Weil L function 133
8.2. Elliptic curves Er 136
8.3. Computing A(p) 138
8.4. A Hecke Grossencharacter 141
8.5. A theta series 142
8.6. The automorphy of / 143
Chapter 9. Spherical Functions 147
9.1. Positive definite quadratic forms 147
9.2. Space spherical functions 150
9.3. The spherical functions reconsidered 155
9.4. Harmonic analysis on the sphere 159
Chapter 10. Theta Functions 165
10.1. Introduction 165
10.2. An inversion formula 166
10.3. The congruent theta functions 168
10.4. The automorphy of theta functions 175
10.5. The standard theta function 176
Chapter 11. Representations by Quadratic Forms 179
11.1. Introduction 179
11.2. Siegel s mass formula 180
11.3. Representations by Eisenstein series and cusp forms 185
11.4. The circle method after Kloosterman 190
11.5. The singular series 196
11.6. Equidistribution of integral points on ellipsoids 199
Chapter 12. Automorphic Forms Associated with Number Fields 203
12.1. Automorphic forms attached to Dirichlet L functions 203
12.2. Hecke L functions with Grossencharacters 206
12.3. Automorphic forms associated with quadratic fields 211
12.4. Class group L functions reconsidered 215
12.5. L functions for genus characters 219
12.6. Automorphic forms of weight one 224
x Contents
Chapter 13. Convolution L functions 231
13.1. Introduction 231
13.2. Rankin Selberg integrals 232
13.3. Selberg s theory of Eisenstein series 235
13.4. Statement of general results 240
13.5. The scattering matrix for T0(N) 240
13.6. Functional equations for the convolution L functions 243
13.7. Metaplectic Eisenstein series 246
13.8. Symmetric power L functions 248
Bibliography 255
Index 257
|
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| author | Iwaniec, Henryk 1947- |
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| classification_rvk | SK 180 SK 780 |
| ctrlnum | (OCoLC)37031015 (DE-599)BVBBV012213668 |
| dewey-full | 512/.7 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 511 - General principles of mathematics |
| dewey-raw | 512/.7 511.33 |
| dewey-search | 512/.7 511.33 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012213668 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:42Z |
| institution | BVB |
| isbn | 0821807773 9780821807774 |
| language | English |
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| physical | XII, 259 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Iwaniec, Henryk 1947- Verfasser (DE-588)141817569 aut Topics in classical automorphic forms Henryk Iwaniec Providence, RI American Math. Soc. 1997 XII, 259 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 17 Formes automorphes Formes automorphes ram Automorphic forms Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2074-1 Graduate studies in mathematics 17 (DE-604)BV009739289 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008276606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iwaniec, Henryk 1947- Topics in classical automorphic forms Graduate studies in mathematics Formes automorphes Formes automorphes ram Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4003972-9 |
| title | Topics in classical automorphic forms |
| title_auth | Topics in classical automorphic forms |
| title_exact_search | Topics in classical automorphic forms |
| title_full | Topics in classical automorphic forms Henryk Iwaniec |
| title_fullStr | Topics in classical automorphic forms Henryk Iwaniec |
| title_full_unstemmed | Topics in classical automorphic forms Henryk Iwaniec |
| title_short | Topics in classical automorphic forms |
| title_sort | topics in classical automorphic forms |
| topic | Formes automorphes Formes automorphes ram Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Formes automorphes Automorphic forms Automorphe Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008276606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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