Introduction to Siegel Modular Forms and Dirichlet Series:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
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| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 182 S. 235 mm x 155 mm |
| ISBN: | 9780387787527 0387787526 9780387787534 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to Siegel Modular Forms and Dirichlet Series |c Anatoli Andrianov |
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| adam_text | Contents
Preface............................................................ vii
Introduction: The Two Features of Arithmetic Zeta Functions........... 1
1 Modular Forms................................................ 7
1.1 The Symplectic Group and the Upper Half-Plane................ 7
1.2 Fundamental Domains for the Modular Group .................. 11
1.3 Modular Forms............................................ 19
2 Dirichlet Series of Modular Forms............................... 41
2.1 Radial Dirichlet Series...................................... 41
2.2 Mellin Transform of Cusp Forms in One Variable................ 44
2.3 Transformations of Lobachevsky Half-Spaces................... 47
2.4 Radial Series and Eisenstein Series............................ 55
2.5 Properties of Radial Series for Sums of Two Squares............. 58
3 Hecke-Shimura Rings of Double Cosets.......................... 63
3.1 An Approach to Multiplicativity.............................. 63
3.2 Abstract Rings of Double Cosets.............................. 66
3.3 Rings of Double Cosets of the General Linear Group............. 75
3.4 Rings of Double Cosets of the Symplectic Group................ 85
3.5 Rings of Triangular-Symplectic Double Cosets.................. 106
4 Hecke Operators...............................................119
4.1 Hecke Operators for Congruence Subgroups....................119
4.2 Action of Hecke Operators for FJ5(q) ..........................125
4.3 Hecke Operators and Siegel Operator..........................130
5 Euler Factorization of Radial Series..............................137
5.1 Radial Series of Genus One and Zeta Functions.................138
5.2 Binary Radial Series and Gaussian Composition.................145
5.3 Zeta Functions of Eigenforms for Genus 2......................165
x Contents
Conclusion: Other Groups, Other Horizons...........................169
Notes .............................................................171
References.........................................................175
Index.............................................................179
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:29:38Z |
| institution | BVB |
| isbn | 9780387787527 0387787526 9780387787534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017056068 |
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| physical | XI, 182 S. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Andrianov, Anatolij N. Verfasser aut Introduction to Siegel Modular Forms and Dirichlet Series Anatoli Andrianov New York, NY Springer 2009 XI, 182 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Universitext Dirichlet series Hecke operators Siegel domains Dirichlet-Reihe (DE-588)4150139-1 gnd rswk-swf Siegel-Modulform (DE-588)4129460-9 gnd rswk-swf Siegel-Modulform (DE-588)4129460-9 s Dirichlet-Reihe (DE-588)4150139-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056068&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andrianov, Anatolij N. Introduction to Siegel Modular Forms and Dirichlet Series Dirichlet series Hecke operators Siegel domains Dirichlet-Reihe (DE-588)4150139-1 gnd Siegel-Modulform (DE-588)4129460-9 gnd |
| subject_GND | (DE-588)4150139-1 (DE-588)4129460-9 |
| title | Introduction to Siegel Modular Forms and Dirichlet Series |
| title_auth | Introduction to Siegel Modular Forms and Dirichlet Series |
| title_exact_search | Introduction to Siegel Modular Forms and Dirichlet Series |
| title_full | Introduction to Siegel Modular Forms and Dirichlet Series Anatoli Andrianov |
| title_fullStr | Introduction to Siegel Modular Forms and Dirichlet Series Anatoli Andrianov |
| title_full_unstemmed | Introduction to Siegel Modular Forms and Dirichlet Series Anatoli Andrianov |
| title_short | Introduction to Siegel Modular Forms and Dirichlet Series |
| title_sort | introduction to siegel modular forms and dirichlet series |
| topic | Dirichlet series Hecke operators Siegel domains Dirichlet-Reihe (DE-588)4150139-1 gnd Siegel-Modulform (DE-588)4129460-9 gnd |
| topic_facet | Dirichlet series Hecke operators Siegel domains Dirichlet-Reihe Siegel-Modulform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056068&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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