Lectures on automorphic L-functions:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2009
|
| Schriftenreihe: | Fields Institute monographs
20 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | XII, 283 S. |
| ISBN: | 9780821848005 0821848003 |
Internformat
MARC
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| 100 | 1 | |a Cogdell, James W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on automorphic L-functions |c James W. Cogdell, Henry H. Kim, M. Ram Murty |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2009 | |
| 300 | |a XII, 283 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fields Institute monographs |v 20 | |
| 500 | |a Includes bibliographical references | ||
| 650 | 0 | 7 | |a Automorphe Funktion |0 (DE-588)4143706-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a L-Funktion |0 (DE-588)4137026-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Kim, Henry Hyeongsin |e Verfasser |4 aut | |
| 700 | 1 | |a Murty, Maruti Ram |d 1953- |e Verfasser |0 (DE-588)120837307 |4 aut | |
| 830 | 0 | |a Fields Institute monographs |v 20 |w (DE-604)BV009737926 |9 20 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020423142&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020423142 | ||
Datensatz im Suchindex
| _version_ | 1804143065166774272 |
|---|---|
| adam_text | Contents
Preface
xi
Lectures on L-functions, Converse
Theorems,
and
Functor
iality for GL(n)
James W. Cogdell
Preface
3
Lecture
1.
Modular
Forms and Their L-functions
5
1.
Examples
б
2.
Growth estimates on cusp forms
7
3.
The L-function of a cusp form
8
4.
The
Euler
product
10
5.
References
12
Lecture
2.
Automorphic Forms
13
1.
Automorphic forms on GLi
13
2.
Automorphic forms on GLn
16
3.
Smooth automorphic forms
17
4.
L2-automorphic forms
18
5.
Cusp forms
18
6.
References
19
Lecture
3.
Automorphic Representations
21
1.
(.nľ-ŕinite)
automorphic representations
21
2.
Smooth automorphic representations
24
3.
L2-automorphic representations
25
4.
Cuspidal representations
25
5.
Connections with classical forms
26
6.
References
27
Lecture
4.
Fourier Expansions and Multiplicity One Theorems
29
1.
The Fourier expansion of a cusp form
29
2.
Whittaker models
31
3.
Multiplicity one for GLn
33
4.
Strong multiplicity ones for GLn
34
5.
References
35
¡
Contents
Lecture
5.
Eulerian Integral Representations
37
1.
GL2
χ
GLX
37
2.
GLn
χ
GLm with m<n
38
3.
GLn
χ
GLn
41
4.
Summary
43
5.
References
43
Lecture
6.
Local L-functions: The Non-Archimedean Case
45
1.
Whittaker functions
45
2.
The local ¿-function (m
<
n)
46
3.
The local functional equation
48
4.
The conductor of
тг
49
5.
Multiplicativity and stability of 7-factors
49
6.
References
50
Lecture
7.
The Unramified Calculation
51
1.
Unramified representations
52
2.
Unramified Whittaker functions
53
3.
Calculating the integral
55
4.
References
57
Lecture
8.
Local L-functions: The Archimedean Case
59
1.
The arithmetic
Langlands
classification
59
2.
The ¿-functions
59
3.
The integrals (m
<
n)
61
4.
Is the ¿-factor correct?
62
5.
References
64
Lecture
9.
Global ¿-functions
65
1.
Convergence
65
2.
Meromorphic continuation
66
3.
Poles of ¿-functions
67
4.
The global functional equation
67
5.
Boundedness in vertical strips
68
6.
Summary
69
7.
Strong Multiplicity One revisited
69
8.
Generalized Strong Multiplicity One
70
9.
References
70
Lecture
10.
Converse Theorems
73
1.
Converse Theorems for GLn
73
2.
Inverting the integral representation
74
3.
Proof of Theorem
10.1
(i)
77
4.
Proof of Theorem
10.1
(ii)
77
5.
Theorem
10.2
and beyond
78
6.
A useful variant
79
7.
Conjectures
79
Contents
vii
8.
References
80
Lecture
11.
Functoriality
81
1.
The Weil-Deligne group
81
2.
The dual group
82
3.
The local
Langlands
conjecture
82
4.
Local functoriality
83
5.
Global functoriality
83
6.
Functoriality and the Converse Theorem
84
7.
References
85
Lecture
12.
Functoriality for the Classical Groups
87
1.
The results
87
2.
Construction of a candidate lift
88
3.
Analytic properties of L-functions
90
4.
Apply the Converse Theorem
90
5.
References
90
Lecture
13.
Functoriality for the Classical Groups, II
91
1.
Functoriality
91
2.
Descent
92
3.
Bounds towards Ramanujan
94
4.
The local converse theorem
94
5.
Further applications
95
6.
References
96
Automorphic L-functions
Henry H. Kim
Introduction
99
Chapter
1.
Chevalley Groups and their Properties
101
1.
Algebraic groups
101
2.
Roots and coroots
103
3.
Classification of root systems
104
4.
Construction of Chevalley groups: simply connected type
107
5.
Structure of parabolic subgroups
108
Chapter
2.
Cuspidal Representations
113
Chapter
3.
Zz-groups and Automorphic i-functions
115
Chapter
4.
Induced Representations
119
1.
Harish-Chandra homomorphisms
119
2.
Induced representations:
F
local
121
3.
Intertwining operators for I(s,
ж)
122
4.
Digression on admissible representations
123
5.
Induced representations:
F
global
126
Contents
Vlil
6.
Induced representations as holomorphic fiber bundles
126
Chapter
5. Eisenstein
Series and Constant Terms
129
1.
Definition of
Eisenstein
series
129
2.
Constant terms
130
3.
Psuedo-Eisenstein series
132
Chapter
6.
L-functions in the Constant Terms
137
List of L-functions via Langlands-Shahidi method
143
Chapter
7.
Meromorphic Continuation of L-functions
145
Chapter
8.
Generic Representations and their Whittaker Models
147
1.
General case
147
2.
Whittaker models for induced representations
149
Chapter
9.
Local Coefficients and Non-constant Terms
153
1.
Non-constant terms of
Eisenstein
series
153
2.
Local coefficients and crude functional equation
158
Chapter
10.
Local
Langlands
Correspondence
161
Chapter
11.
Local L-functions and Functional Equations
165
1.
Definition of local L-functions
169
2.
Properties of local L-functions; supercuspidal representations
170
Chapter
12.
Normalization of Intertwining Operators
171
1.
π
is supercuspidal
171
2.
π
is tempered, generic
171
3.
π
is non-tempered, generic
172
4.
Application to reducibility criterion
175
Chapter
13.
Holomorphy and Bounded in Vertical Strips
177
1.
Holomorphy of L-functions
177
2.
Boundedness in vertical strips of L-functions
177
Chapter
14. Langlands
Functoriality Conjecture
181
Chapter
15.
Converse Theorem of Cogdell and Piatetski-Shapiro
183
Chapter
16.
Functoriality of the Symmetric Cube
187
1.
Weak Ramanujan property
187
2.
Functoriality of the symmetric square
187
3.
Functoriality of the tensor product of GL^
x
GL%
188
4.
Functoriality of the symmetric cube
190
Chapter
17.
Functoriality of the Symmetric Fourth
193
1.
Functoriality of the exterior square
193
Contents ix
2.
Functoriality of the symmetric fourth
194
Bibliography
199
Applications of Symmetric Power ¿-functions
M. Ram Murty
Preface
205
Lecture
1.
The Sato-Tate Conjecture
207
1.
Introduction
207
2.
Uniform distribution
208
3.
Wiener-Ikehara Tauberian theorem
209
4.
Weyl s theorem for compact groups
210
Lecture
2.
Maass Wave Forms
213
1.
Maass forms of weight zero
213
2.
Maass forms with weight
214
3. Eisenstein
series
214
4.
Upper bound for Fourier coefficients and eigenvalue estimators
216
Lecture
3.
The Rankin-Selberg Method
219
1. Eisenstein
series and non-vanishing of C(,s) on 9t(s)
= 1 219
2.
Explicit construction of Maass cusp forms
221
3.
The Rankin-Selberg ¿-function
222
4.
Rankin-Selberg ¿-functions for GLn
225
Lecture
4.
Oscillations of Fourier Coefficients of Cusp Forms
227
1.
Preliminaries
227
2.
Rankin s theorem
228
3.
A review of symmetric power ¿-functions
230
4.
Proof of Theorem
4.1 232
Lecture
5.
Poincaré
Series
237
1.
Poincaré
series for SL2(Z)
237
2.
Fourier coefficients and
Kloosterman
sums
239
3.
The Kloosterman-Selberg
zeta
function
242
Lecture
6.
Kloosterman
Sums and Selberg s Conjecture
243
1.
Petersson:s formula
243
2.
Selberg s
theorem
244
3.
The Selberg-Linnik conjecture
245
Lecture
7.
Refined Estimates for Fourier Coefficients of Cusp Forms
247
1.
Sieve theory and
Kloosterman
sums
247
2.
Gauss sums and hyper-Kloosterman sum
248
3.
The Duke-Iwaniec method
248
x
Contents
Lecture
8.
Twisting and Averaging of L-series
253
1.
Selberg conjectures for GLn
253
2.
Ramanujan conjecture for Gln
254
3.
The method of averaging L-functions
255
Lecture
9.
The Kim-Samak Theorem
257
1.
Preliminaries
257
2.
Rankin-Selberg theory
258
3.
An application of the Duke-Iwaniec method
259
Lecture
10.
Introduction to Artin L-functions
265
1. Hecke
L-functions
265
2.
Artin L-functions
266
3.
Automorphic induction and Artin s conjecture
268
Lecture
11.
Zeros and Poles of Artin L-functions
271
1.
The
Heilbronn
character
271
2.
The fundamental inequality
272
3.
Rankin-Selberg property for Galois representations
273
Lecture
12.
The Langlands-Tunnell Theorem
275
1.
Review of some group theory
275
2.
Some representation theory
276
3.
An application of the Deligne-Serre theory
277
4.
The general case
277
5.
Sarnak s theorem
278
Bibliography
281
|
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| id | DE-604.BV036500714 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:41:44Z |
| institution | BVB |
| isbn | 9780821848005 0821848003 |
| language | English |
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| physical | XII, 283 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Fields Institute monographs |
| series2 | Fields Institute monographs |
| spelling | Cogdell, James W. Verfasser aut Lectures on automorphic L-functions James W. Cogdell, Henry H. Kim, M. Ram Murty Providence, R.I. American Mathematical Society 2009 XII, 283 S. txt rdacontent n rdamedia nc rdacarrier Fields Institute monographs 20 Includes bibliographical references Automorphe Funktion (DE-588)4143706-8 gnd rswk-swf L-Funktion (DE-588)4137026-0 gnd rswk-swf L-Funktion (DE-588)4137026-0 s Automorphe Funktion (DE-588)4143706-8 s b DE-604 Kim, Henry Hyeongsin Verfasser aut Murty, Maruti Ram 1953- Verfasser (DE-588)120837307 aut Fields Institute monographs 20 (DE-604)BV009737926 20 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020423142&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cogdell, James W. Kim, Henry Hyeongsin Murty, Maruti Ram 1953- Lectures on automorphic L-functions Fields Institute monographs Automorphe Funktion (DE-588)4143706-8 gnd L-Funktion (DE-588)4137026-0 gnd |
| subject_GND | (DE-588)4143706-8 (DE-588)4137026-0 |
| title | Lectures on automorphic L-functions |
| title_auth | Lectures on automorphic L-functions |
| title_exact_search | Lectures on automorphic L-functions |
| title_full | Lectures on automorphic L-functions James W. Cogdell, Henry H. Kim, M. Ram Murty |
| title_fullStr | Lectures on automorphic L-functions James W. Cogdell, Henry H. Kim, M. Ram Murty |
| title_full_unstemmed | Lectures on automorphic L-functions James W. Cogdell, Henry H. Kim, M. Ram Murty |
| title_short | Lectures on automorphic L-functions |
| title_sort | lectures on automorphic l functions |
| topic | Automorphe Funktion (DE-588)4143706-8 gnd L-Funktion (DE-588)4137026-0 gnd |
| topic_facet | Automorphe Funktion L-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020423142&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009737926 |
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