Modular forms and Hecke operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1995
|
| Series: | Translations of mathematical monographs
145 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | VII, 334 S. |
| ISBN: | 0821802771 |
Staff View
MARC
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| 240 | 1 | 0 | |a Moduljarnye formy i operatory Gekke |
| 245 | 1 | 0 | |a Modular forms and Hecke operators |c A. N. Andrianov ; V. G. Zhuravlev |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1995 | |
| 300 | |a VII, 334 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 145 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Formes modulaires | |
| 650 | 7 | |a Formes modulaires |2 ram | |
| 650 | 7 | |a Hecke, opérateurs de |2 ram | |
| 650 | 7 | |a Hecke-operatoren |2 gtt | |
| 650 | 7 | |a Modulaire krommen |2 gtt | |
| 650 | 7 | |a Vormen (wiskunde) |2 gtt | |
| 650 | 4 | |a Forms, Modular | |
| 650 | 4 | |a Hecke operators | |
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Record in the Search Index
| _version_ | 1804124979446415360 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Theta Series 3
§1. Definition of theta series 3
1. Representations of quadratic forms by quadratic forms 3
2. Definition of theta series 5
§2. Symplectic transformations 6
1. The symplectic group 6
2. The Siegel upper half plane 8
§3. Symplectic transformations of theta series 11
1. Transformations of theta series 11
2. The Siegel modular group and the theta group 16
3. Symplectic transformations of theta series 19
§4. Computation of the multiplier 25
1. Automorphy factors 25
2. Quadratic forms of level 1 27
3. The multiplier as a Gauss sum 28
4. Quadratic forms in an even number of variables 32
5. Quadratic forms in an odd number of variables 37
Chapter 2. Modular Forms 43
§ 1. Fundamental domains for subgroups of the modular group 43
1. The modular triangle 43
2. The Minkowski reduction domain 46
3. The fundamental domain for the Siegel modular group 52
4. Subgroups of finite index 57
§2. Definition of modular forms 59
1. Congruence subgroups of the modular group 59
2. Modular forms of integer weight 60
3. Definition of modular forms of half integer weight 60
4. Theta series as modular forms 60
§3. Fourier expansions 61
1. Modular forms for triangular subgroups 61
2. The Koecher effect 62
3. Fourier expansions of modular forms 65
4. The Siegel operator 72
5. Cusp forms 75
vi CONTENTS
§4. Spaces of modular forms 79
1. Zeros of modular forms for F1 79
2. Modular forms with zero initial Fourier coefficients 82
3. Finite dimensionality of the spaces of modular forms 85
§5. Scalar product and orthogonal decomposition 86
1. The scalar product 87
2. The orthogonal complement 90
Chapter 3. Hecke Rings 93
§1. Abstract Hecke rings 93
1. Averaging over double cosets 93
2. Hecke rings 94
3. The imbedding e 100
4. The anti isomorphism j 101
5. Representations in spaces of automorphic forms 103
6. Hecke algebras over a commutative ring 104
§2. Hecke rings for the general linear group 105
1. Global rings 105
2. Local rings 111
3. The spherical map 117
§3. Hecke rings for the symplectic group 122
1. Global rings 122
2. Local rings 133
3. The spherical map 138
§4. Hecke rings for the symplectic covering group 155
1. Global rings 155
2. Local rings 163
3. The spherical map 175
§5. Hecke rings for the triangular subgroup of the symplectic group 179
1. Global rings 179
2. Local rings 185
3. Expansion of T {m) for n = 1,2 190
§6. Hecke polynomials for the symplectic group 192
1. Negative powers of Frobenius elements 192
2. Factorization of Hecke polynomials 199
3. Symmetric factorization of the polynomials Qnp(v) for « = 1,2 202
4. Coefficients in the factorization of Rankin polynomials 204
5. Symmetric factorization of Rankin polynomials 220
Chapter 4. Hecke Operators 225
§ 1. Hecke operators for congruence subgroups of the modular group 225
1. Hecke operators 225
2. Invariant subspaces and eigenfunctions 229
§2. Action of the Hecke operators 234
1. Hecke operators for Fgfo) 234
2. Hecke operators for Tg 236
3. Hecke operators and the Siegel operator 243
4. Action of the middle factor in the symmetric factorization of Rankin
polynomials 253
CONTENTS vii
§3. Multiplicative properties of the Fourier coefficients 270
1. Modular forms in one variable 271
2. Modular forms of degree 2, Gaussian composition, and zeta functions 279
3. Modular forms of arbitrary degree and even zeta functions 297
Appendix 1. Symmetric Matrices Over a Field 307
1. Arbitrary fields 307
2. The field of real numbers 308
Appendix 2. Quadratic Spaces 311
1. Geometrical language 311
2. Nondegenerate spaces 314
3. Gauss sums 316
4. Isotropy subspaces of nondegenerate spaces over residue fields 318
Appendix 3. Modules in Quadratic Fields and Binary Quadratic Forms 321
1. Modules in algebraic number fields 321
2. Modules and primes in quadratic fields 321
3. Modules in imaginary quadratic fields, and quadratic forms 322
Notes 325
References 329
List of Notation 333
|
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| author | Andrianov, Anatolij N. Žuravlev, Vladimir G. |
| author_facet | Andrianov, Anatolij N. Žuravlev, Vladimir G. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/44 |
| dewey-search | 512.9/44 |
| dewey-sort | 3512.9 244 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV010513183 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:54:16Z |
| institution | BVB |
| isbn | 0821802771 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007007117 |
| oclc_num | 32779307 |
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| physical | VII, 334 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Andrianov, Anatolij N. Verfasser aut Moduljarnye formy i operatory Gekke Modular forms and Hecke operators A. N. Andrianov ; V. G. Zhuravlev Providence, RI American Math. Soc. 1995 VII, 334 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 145 Aus dem Russ. übers. Formes modulaires Formes modulaires ram Hecke, opérateurs de ram Hecke-operatoren gtt Modulaire krommen gtt Vormen (wiskunde) gtt Forms, Modular Hecke operators Hecke-Operator (DE-588)4135665-2 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Modulform (DE-588)4128299-1 s Hecke-Operator (DE-588)4135665-2 s DE-604 Žuravlev, Vladimir G. Verfasser aut Translations of mathematical monographs 145 (DE-604)BV000002394 145 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007007117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andrianov, Anatolij N. Žuravlev, Vladimir G. Modular forms and Hecke operators Translations of mathematical monographs Formes modulaires Formes modulaires ram Hecke, opérateurs de ram Hecke-operatoren gtt Modulaire krommen gtt Vormen (wiskunde) gtt Forms, Modular Hecke operators Hecke-Operator (DE-588)4135665-2 gnd Modulform (DE-588)4128299-1 gnd |
| subject_GND | (DE-588)4135665-2 (DE-588)4128299-1 |
| title | Modular forms and Hecke operators |
| title_alt | Moduljarnye formy i operatory Gekke |
| title_auth | Modular forms and Hecke operators |
| title_exact_search | Modular forms and Hecke operators |
| title_full | Modular forms and Hecke operators A. N. Andrianov ; V. G. Zhuravlev |
| title_fullStr | Modular forms and Hecke operators A. N. Andrianov ; V. G. Zhuravlev |
| title_full_unstemmed | Modular forms and Hecke operators A. N. Andrianov ; V. G. Zhuravlev |
| title_short | Modular forms and Hecke operators |
| title_sort | modular forms and hecke operators |
| topic | Formes modulaires Formes modulaires ram Hecke, opérateurs de ram Hecke-operatoren gtt Modulaire krommen gtt Vormen (wiskunde) gtt Forms, Modular Hecke operators Hecke-Operator (DE-588)4135665-2 gnd Modulform (DE-588)4128299-1 gnd |
| topic_facet | Formes modulaires Hecke, opérateurs de Hecke-operatoren Modulaire krommen Vormen (wiskunde) Forms, Modular Hecke operators Hecke-Operator Modulform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007007117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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