Siegel modular forms: a classical and representation-theoretic approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2019]
|
| Series: | Lecture notes in mathematics
volume 2240 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 131-135 "These lecture notes are based on my workshop on Siegel modular forms at IISER, Pune, India from August 8 to 18, 2017" (Vorwort) |
| Physical Description: | ix, 138 Seiten |
| ISBN: | 9783030156749 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction to Siegel Modular Forms I
1 1 Motivation 1
1 2 The Symplectic Group 3
1 3 Siegel Upper Half-Space 4
1 4 Siegel Modular Forms 5
2 Examples 9
2 1 Examples 9
211 Theta Series 9
212 Eisenstein Series 9
213 Saito-Kurokawa Lifts 11
2 2 Congruence Subgroups 12
221 Congruence Subgroups in Genus 2 12
222 Siegel Modular Forms with Level 13
3 Hecke Theory and /--Functions 15
3 1 The Hecke Algebra 15
3 2 Action of the Hecke Algebra on Siegel Modular Forms 17
3 3 Relation Between Fourier Coefficients and Hecke
Eigenvalues for Genus 2 19
34/ -Functions 20
341/ -Function for Saito-Kurokawa Lifts 22
4 Nonvanishing of Fourier Coefficients and Applications 23
4 1 Generalized Ramanujan Conjecture 23
4 2 Nonvanishing of Fourier Coefficients 24
4 3 Application of the Nonvanishing Result 27
4 4 Böcherer’s Conjecture 29
5 Applications of Properties of / -Functions 31
5 1 Determining Cusp Forms by Size of Fourier Coefficients 31
5 2 Sign Changes of Hecke Eigenvalues 33
5 3 Sign Changes of Fourier Coefficients 35
v
vi Contents
6 Cuspidal Automorphic Representations Corresponding
to Siegel Modular Forms 39
6 1 Classical to Adelic 39
6 2 Hecke Equivariance 43
6 3 Satake Isomorphism 44
6 4 Spherical Representations 46
6 5 The Representation Associated to a Siegel Cusp Form 47
7 Local Representation Theory of GSp4 ( Qp) 49
7 1 Local Non-archimedean Representations for GSp4 49
7 2 Generic Representations 52
7 3 Iwahori-Spherical Representations 54
7 4 Paramodular Theory 57
8 Bessel Models and Applications 63
8 1 The L-Function L(s, ay x r) 63
8 2 Definition of Global Bessel Model 66
8 3 Local Bessel Model 68
8 4 Explicit Formulas for Distinguished Vectors in Local
Bessel Models 70
9 Analytic and Arithmetic Properties of GSp4 x GL2
L-Functions 75
9 1 Functional Equation and Analytic Continuation 75
9 2 Transfer to GL4 76
9 3 Other Analytic Applications 77
9 4 Arithmetic Applications of the Integral Representation
of L(s, TTp x t) 80
10 Integral Representation of the Standard L-Function 83
10 1 The zeta integral 83
10 2 The Basic Identity 84
10 3 The Local Integral Computation 86
10 4 Global Integral Representation 88
10 5 Classical Reformulation 89
10 6 Arithmetic Results in Genus 2 89
Appendix A: GL2 Notes: Classical Modular Forms 93
Appendix B: The p-Adic Fields Q, and the Ring of Adeles A or Q________ 97
Appendix C: GL2 Notes: Representation Theory 99
Appendix D: Solutions to Exercises 103
References 131
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| id | DE-604.BV045903873 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:29:54Z |
| institution | BVB |
| isbn | 9783030156749 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031286630 |
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| physical | ix, 138 Seiten |
| publishDate | 2019 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
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| spelling | Pitale, Ameya 1977- (DE-588)106023114X aut Siegel modular forms a classical and representation-theoretic approach Ameya Pitale Cham Springer [2019] © 2019 ix, 138 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics volume 2240 Literaturverzeichnis: Seite 131-135 "These lecture notes are based on my workshop on Siegel modular forms at IISER, Pune, India from August 8 to 18, 2017" (Vorwort) Siegel-Modulform (DE-588)4129460-9 gnd rswk-swf Siegel-Modulform (DE-588)4129460-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-15675-6 Lecture notes in mathematics volume 2240 (DE-604)BV000676446 2240 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031286630&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pitale, Ameya 1977- Siegel modular forms a classical and representation-theoretic approach Lecture notes in mathematics Siegel-Modulform (DE-588)4129460-9 gnd |
| subject_GND | (DE-588)4129460-9 |
| title | Siegel modular forms a classical and representation-theoretic approach |
| title_auth | Siegel modular forms a classical and representation-theoretic approach |
| title_exact_search | Siegel modular forms a classical and representation-theoretic approach |
| title_full | Siegel modular forms a classical and representation-theoretic approach Ameya Pitale |
| title_fullStr | Siegel modular forms a classical and representation-theoretic approach Ameya Pitale |
| title_full_unstemmed | Siegel modular forms a classical and representation-theoretic approach Ameya Pitale |
| title_short | Siegel modular forms |
| title_sort | siegel modular forms a classical and representation theoretic approach |
| title_sub | a classical and representation-theoretic approach |
| topic | Siegel-Modulform (DE-588)4129460-9 gnd |
| topic_facet | Siegel-Modulform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031286630&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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