Arithmeticity in the theory of automorphic forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2000
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| Series: | Mathematical surveys and monographs
Volume 82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 302 Seiten |
| ISBN: | 0821826719 9780821849613 |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Preface vii
Notation and Terminology ix
Introduction 1
Chapter I. Automorphic Forms and Families of Abelian
Varieties 7
1. Algebraic preliminaries 7
2. Polarized abelian varieties 13
3. Symmetric spaces and factors of automorphy 17
4. Families of polarized abelian varieties 22
5. Definition of automorphic forms 30
6. Parametrization by theta functions 37
Chapter II. Arithmeticity of Automorphic Forms 45
7. The field A(Qab) _ 45
8. Action of certain elements of Ga on R 50
9. The reciprocity law at CM points and rationality of auto¬
morphic forms 58
10. Automorphisms of the spaces of automorphic forms 67
11. Arithmeticity at CM points 76
Chapter III. Arithmetic of Differential Operators and
Nearly Holomorphic Functions 87
12. Differential operators on symmetric spaces 87
13. Nearly holomorphic functions 98
14. Arithmeticity of nearly holomorphic functions 107
15. Holomorphic projection 122
Chapter IV. Eisenstein Series of Simpler Types 127
16. Eisenstein series on U(r]n) 127
17. Arithmeticity and near holomorphy of Eisenstein series 137
18. Eisenstein series in the Hilbert modular case 149
Chapter V. Zeta Functions Associated with Hecke
Eigenforms 159
19. Formal Euler products and generalized Mobius functions 159
20. Dirichlet series obtained from Hecke eigenvalues and
Fourier coefficients 166
21. The Euler products for the forms of half integral weight 175
22. The largest possible pole of Z(s, f, ) 177
V
vi CONTENTS
Chapter VI. Analytic Continuation and Near Holomor
phy of Eisenstein Series of General Types 185
23. Eisenstein series of general types 185
24. Pullback of Eisenstein series 194
25. Proof of Theorems in Sections 20 and 23 203
26. Near holomorphy of Eisenstein series in Case UB 208
Chapter VII. Arithmeticity of the Critical Values of
Zeta Functions and Eisenstein Series of General Types 219
27. The spaces of holomorphic Eisenstein series 219
28. Main theorems on arithmeticity in Cases SP and UT 230
29. Main theorems on arithmeticity in Case UB 240
Appendix 247
Al. The series associated to a symmetric matrix and Gauss
sums 247
A2. Metaplectic groups and factors of automorphy 251
A3. Transformation formulas of general theta series 262
A4. The constant term of a theta series at each cusp depends
only on the genus 272
A5. Theta series of a hermitian form 274
A6. Estimate of the Fourier coefficients of a modular form 278
A7. The Mellin transforms of Hilbert modular forms 282
A8. Certain unitarizable representation spaces 285
References 297
Index 301
|
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| indexdate | 2024-07-09T18:43:07Z |
| institution | BVB |
| isbn | 0821826719 9780821849613 |
| language | English |
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| physical | x, 302 Seiten |
| publishDate | 2000 |
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| series2 | Mathematical surveys and monographs |
| spelling | Shimura, Goro 1930-2019 Verfasser (DE-588)12425067X aut Arithmeticity in the theory of automorphic forms Goro Shimura Providence, Rhode Island American Mathematical Society 2000 © 2000 x, 302 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 82 Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1309-5 Mathematical surveys and monographs Volume 82 (DE-604)BV000018014 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057697&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shimura, Goro 1930-2019 Arithmeticity in the theory of automorphic forms Mathematical surveys and monographs Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4003972-9 |
| title | Arithmeticity in the theory of automorphic forms |
| title_auth | Arithmeticity in the theory of automorphic forms |
| title_exact_search | Arithmeticity in the theory of automorphic forms |
| title_full | Arithmeticity in the theory of automorphic forms Goro Shimura |
| title_fullStr | Arithmeticity in the theory of automorphic forms Goro Shimura |
| title_full_unstemmed | Arithmeticity in the theory of automorphic forms Goro Shimura |
| title_short | Arithmeticity in the theory of automorphic forms |
| title_sort | arithmeticity in the theory of automorphic forms |
| topic | Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Automorphe Form |
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