Automorphic forms and applications:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2007
|
| Schriftenreihe: | IAS Park City mathematics series
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | XIV, 427 S. |
| ISBN: | 9780821828731 0821828738 |
Internformat
MARC
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| 245 | 1 | 0 | |a Automorphic forms and applications |c Peter Sarnak ... eds. |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2007 | |
| 300 | |a XIV, 427 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a IAS Park City mathematics series |v 12 | |
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Fonctions automorphes | |
| 650 | 4 | |a Formes (Mathématiques) | |
| 650 | 4 | |a Formes automorphes | |
| 650 | 4 | |a Automorphic forms | |
| 650 | 4 | |a Automorphic functions | |
| 650 | 4 | |a Forms (Mathematics) | |
| 650 | 0 | 7 | |a Automorphe Form |0 (DE-588)4003972-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Automorphe Form |0 (DE-588)4003972-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sarnak, Peter |d 1953- |e Sonstige |0 (DE-588)102958365X |4 oth | |
| 830 | 0 | |a IAS Park City mathematics series |v 12 |w (DE-604)BV010402400 |9 12 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015682110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805074100839776256 |
|---|---|
| adam_text |
Contents
Preface xiii
Introduction 1
Armand Borel, Automorphic Forms on Reductive Groups 5
Introduction 7
1. Notation 7
2. Notion of automorphic form 8
3. First properties of automorphic forms 9
4. Reductive groups (review) 12
5. Arithmetic subgroups. Reduction theory 19
6. Constant terms. The basic estimate 24
7. Finite dimensionality of A(T, J, £) 28
8. Convolution Operators on cuspidal functions 29
9. Automorphic forms and the regulär representation on T\G 30
10. A decomposition of the space of automorphic forms. 32
11. Some estimates of growth functions 33
12. Eisenstein series 35
Bibliography 39
L. Clozel, Spectral Theory of Automorphic Forms 41
Foreword 43
Lecture 1. Mostly SL(2) 47
x CONTENTS
Lecture 2. The spectral decomposition of L2(G(Q)\G(A)):
Arthur's conjectures 57
Lecture 3. Known bounds for the cuspidal spectrum and the Burger Sarnak
method 65
Lecture 4. Applications: control of the spectrum 79
Appendix: All reductive adelic groups are tarne 87
Bibliography 89
James W. Cogdell, L functions and Converse Theorems for GL„ 95
Introduction 97
Lecture 1. Fourier expansions and multiplicity one 101
Lecture 2. Eulerian integrals for GLn 111
Lecture 3. Local L functions 123
Lecture 4. Global L functions 137
Lecture 5. Converse theorems 147
Lecture 6. Converse theorems and functoriality 161
Bibliography 173
Philippe Michel, Analytic Number Theory and Families of
Automorphic L functions 179
Foreword 181
Lecture 1. Analytic properties of individual L functions 187
Lecture 2. A review of classical automorphic forms 211
Lecture 3. Large sieve inequalities 223
Lecture 4. The subconvexity problem 241
Lecture 5. Some applications of subconvexity 267
Bibliography 285
Freydoon Shahidi, Langlands Shahidi Method 297
Foreword 299
Lecture 1. Basic concepts 301
Lecture 2. Eisenstein series and L functions 307
Lecture 3. Functional equations and multiplicativity 315
CONTENTS xi
Lecture 4. Holomorphy and boundedness; applications 321
Bibliography 327
Audrey Terras, Arithmetical Quantum Chaos 331
Abstract 333
Lecture 1. Finite modeis 335
Lecture 2. Three Symmetrie Spaces 355
Bibliography 371
David A. Vogan, Jr, Isolated Unitary Representations. 377
Bibliography 397
Wen Ching Winnie Li, Ramanujan Graphs and Ramanujan
Hypergraphs 399
Introduction 401
Lecture 1. Ramanujan graphs and connections with number theory 403
Lecture 2. Ramanujan hypergraphs 415
Bibliography 425 |
| adam_txt |
Contents
Preface xiii
Introduction 1
Armand Borel, Automorphic Forms on Reductive Groups 5
Introduction 7
1. Notation 7
2. Notion of automorphic form 8
3. First properties of automorphic forms 9
4. Reductive groups (review) 12
5. Arithmetic subgroups. Reduction theory 19
6. Constant terms. The basic estimate 24
7. Finite dimensionality of A(T, J, £) 28
8. Convolution Operators on cuspidal functions 29
9. Automorphic forms and the regulär representation on T\G 30
10. A decomposition of the space of automorphic forms. 32
11. Some estimates of growth functions 33
12. Eisenstein series 35
Bibliography 39
L. Clozel, Spectral Theory of Automorphic Forms 41
Foreword 43
Lecture 1. Mostly SL(2) 47
x CONTENTS
Lecture 2. The spectral decomposition of L2(G(Q)\G(A)):
Arthur's conjectures 57
Lecture 3. Known bounds for the cuspidal spectrum and the Burger Sarnak
method 65
Lecture 4. Applications: control of the spectrum 79
Appendix: All reductive adelic groups are tarne 87
Bibliography 89
James W. Cogdell, L functions and Converse Theorems for GL„ 95
Introduction 97
Lecture 1. Fourier expansions and multiplicity one 101
Lecture 2. Eulerian integrals for GLn 111
Lecture 3. Local L functions 123
Lecture 4. Global L functions 137
Lecture 5. Converse theorems 147
Lecture 6. Converse theorems and functoriality 161
Bibliography 173
Philippe Michel, Analytic Number Theory and Families of
Automorphic L functions 179
Foreword 181
Lecture 1. Analytic properties of individual L functions 187
Lecture 2. A review of classical automorphic forms 211
Lecture 3. Large sieve inequalities 223
Lecture 4. The subconvexity problem 241
Lecture 5. Some applications of subconvexity 267
Bibliography 285
Freydoon Shahidi, Langlands Shahidi Method 297
Foreword 299
Lecture 1. Basic concepts 301
Lecture 2. Eisenstein series and L functions 307
Lecture 3. Functional equations and multiplicativity 315
CONTENTS xi
Lecture 4. Holomorphy and boundedness; applications 321
Bibliography 327
Audrey Terras, Arithmetical Quantum Chaos 331
Abstract 333
Lecture 1. Finite modeis 335
Lecture 2. Three Symmetrie Spaces 355
Bibliography 371
David A. Vogan, Jr, Isolated Unitary Representations. 377
Bibliography 397
Wen Ching Winnie Li, Ramanujan Graphs and Ramanujan
Hypergraphs 399
Introduction 401
Lecture 1. Ramanujan graphs and connections with number theory 403
Lecture 2. Ramanujan hypergraphs 415
Bibliography 425 |
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| isbn | 9780821828731 0821828738 |
| language | English |
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| series | IAS Park City mathematics series |
| series2 | IAS Park City mathematics series |
| spelling | Automorphic forms and applications Peter Sarnak ... eds. Providence, RI American Math. Soc. 2007 XIV, 427 S. txt rdacontent n rdamedia nc rdacarrier IAS Park City mathematics series 12 Includes bibliographical references Fonctions automorphes Formes (Mathématiques) Formes automorphes Automorphic forms Automorphic functions Forms (Mathematics) Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Sarnak, Peter 1953- Sonstige (DE-588)102958365X oth IAS Park City mathematics series 12 (DE-604)BV010402400 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015682110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Automorphic forms and applications IAS Park City mathematics series Fonctions automorphes Formes (Mathématiques) Formes automorphes Automorphic forms Automorphic functions Forms (Mathematics) Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4003972-9 |
| title | Automorphic forms and applications |
| title_auth | Automorphic forms and applications |
| title_exact_search | Automorphic forms and applications |
| title_exact_search_txtP | Automorphic forms and applications |
| title_full | Automorphic forms and applications Peter Sarnak ... eds. |
| title_fullStr | Automorphic forms and applications Peter Sarnak ... eds. |
| title_full_unstemmed | Automorphic forms and applications Peter Sarnak ... eds. |
| title_short | Automorphic forms and applications |
| title_sort | automorphic forms and applications |
| topic | Fonctions automorphes Formes (Mathématiques) Formes automorphes Automorphic forms Automorphic functions Forms (Mathematics) Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Fonctions automorphes Formes (Mathématiques) Formes automorphes Automorphic forms Automorphic functions Forms (Mathematics) Automorphe Form |
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