Analytic properties of automorphic L-functions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Acad. Press
1988
|
| Schriftenreihe: | Perspectives in mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 131 S. |
| ISBN: | 0122791754 |
Internformat
MARC
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| 100 | 1 | |a Gelbart, Stephen S. |d 1946- |e Verfasser |0 (DE-588)108684083 |4 aut | |
| 245 | 1 | 0 | |a Analytic properties of automorphic L-functions |c Stephen Gelbart ; Freydoon Shahidi |
| 264 | 1 | |a Boston [u.a.] |b Acad. Press |c 1988 | |
| 300 | |a VII, 131 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Perspectives in mathematics |v 6 | |
| 650 | 7 | |a Fonctions L |2 ram | |
| 650 | 7 | |a Fonctions automorphes |2 ram | |
| 650 | 4 | |a Automorphic functions | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
ACKNOWLEDGEMENTS vii
INTRODUCTION 1
CHAPTER I. FIRST STEPS (1965 1970) 5
§1. An analysis of the method of Jacquet Langlands 5
1.1. Cuspidal representations and L functions for GL(2) ... 5
1.2. Global zeta integrals and their factorization 8
1.3. The local zeta integrals 11
1.4. More local theory 12
1.5. Global results for Lg(s, n) 15
1.6. Global results for L{s,ir) 16
1.7. Description of the L function machine 19
§2. Eisenstein series and Langlands Eider Products 21
2.1. The example of L(s,x) 21
2.2. L groups 23
2.3. Unramified representations 25
2.4. The general set up: Preliminary definitions 30
2.5. The general set up: Eisenstein series, constant terms,
and Langlands Euler products 33
CHAPTER II. DEVELOPMENTS AND
REFINEMENTS (1970 1982) 41
§1. Zeta integrals for GL(n) and related groups 41
1.1. The method of Tate Godement Jacquet 41
1.2. Jacquet s theory for GL(2) x Gl(2) and the method of
Rankin Selberg 44
Appendix to Section (1.2): Analysis and reformulation of the
method of Rankin Selberg Jacquet for GL(2) x GL(2) 47
1.3. Shimura s method 59
1.4. Hecke theory for GL(n) 61
1.5. The metaplectic group 63
1.6. Symmetric powers of L functions 65
1.7. GL(n) x GL(m) 67
1.8. Additional notes and references: ^ functions and the
lifting problem 70
1.9. Concluding remarks 72
§2. Eisenstein series and generic representations 75
2.1. Whittaker models: General notions 75
2.2. Whittaker models for 7(5,7r«) 77
2.3. Fourier coefficients of Eisenstein series 78
2.4. Local coefficients and the functional equation
for Ls(s,tt) 79
2.5. Examples 82
2.6. On the non vanishing of i functions for Re(s) = 1 84
CHAPTER III. RECENT DEVELOPMENTS (1982 ) 87
§1. Explicit Construction of Zeta integrals
a la Piatetski Shapiro 87
1.1. Origins of the method of Piatetski Shapiro and Rallis 87
1.2. The construction of Piatetski Shapiro and Rallis 90
1.3. Summing up of the method 93
1.4. Rankin triple products 94
1.5. X functions for G x GL(n) 97
§2. Langlands Theory Completed 102
2.1. Range of applicability of the method 102
2.2. A uniform line of convergence for Lg(s, t, r) 105
2.3. Ramanujan type estimates 107
2.4. Analytic continuation of the completed L function .. 109
2.5. More examples 112
2.6. On the uniqueness of local factors 113
Last Words 116
REFERENCES 119
INDEX 129
|
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| id | DE-604.BV003709167 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:12Z |
| institution | BVB |
| isbn | 0122791754 |
| language | English |
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| physical | VII, 131 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Acad. Press |
| record_format | marc |
| series | Perspectives in mathematics |
| series2 | Perspectives in mathematics |
| spelling | Gelbart, Stephen S. 1946- Verfasser (DE-588)108684083 aut Analytic properties of automorphic L-functions Stephen Gelbart ; Freydoon Shahidi Boston [u.a.] Acad. Press 1988 VII, 131 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematics 6 Fonctions L ram Fonctions automorphes ram Automorphic functions L-functions Automorphe L-Funktion (DE-588)4208075-7 gnd rswk-swf Automorphe L-Funktion (DE-588)4208075-7 s DE-604 Shahidi, Freydoon 1947- Verfasser (DE-588)128913711 aut Perspectives in mathematics 6 (DE-604)BV000770492 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002361186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gelbart, Stephen S. 1946- Shahidi, Freydoon 1947- Analytic properties of automorphic L-functions Perspectives in mathematics Fonctions L ram Fonctions automorphes ram Automorphic functions L-functions Automorphe L-Funktion (DE-588)4208075-7 gnd |
| subject_GND | (DE-588)4208075-7 |
| title | Analytic properties of automorphic L-functions |
| title_auth | Analytic properties of automorphic L-functions |
| title_exact_search | Analytic properties of automorphic L-functions |
| title_full | Analytic properties of automorphic L-functions Stephen Gelbart ; Freydoon Shahidi |
| title_fullStr | Analytic properties of automorphic L-functions Stephen Gelbart ; Freydoon Shahidi |
| title_full_unstemmed | Analytic properties of automorphic L-functions Stephen Gelbart ; Freydoon Shahidi |
| title_short | Analytic properties of automorphic L-functions |
| title_sort | analytic properties of automorphic l functions |
| topic | Fonctions L ram Fonctions automorphes ram Automorphic functions L-functions Automorphe L-Funktion (DE-588)4208075-7 gnd |
| topic_facet | Fonctions L Fonctions automorphes Automorphic functions L-functions Automorphe L-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002361186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000770492 |
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