Lectures on Automorphic L-functions (Google eBook)

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American Mathematical Soc. - Mathematics - 283 pages
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James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography
  

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Contents

Lectures on Lfunctions Converse Theorems and Functoriality for GLn
1
Modular Forms and Their Lfunctions
5
Automorphic Forms
13
Automorphic Representations
21
Fourier Expansions and Multiplicity One Theorems
29
Eulerian Integral Representations
37
Local Lfunctions The NonArchimedean Case
45
The Unramified Calculation
51
Local Coefficients and Nonconstant Terms
153
Local Langlands Correspondence
161
Local Lfunctions and Functional Equations
165
Normalization of Intertwining Operators
171
Holomorphy and Bounded in Vertical Strips
177
Langlands Functoriality Conjecture
181
Converse Theorem of Cogdell and PiatetskiShapiro
183
Functoriality of the Symmetric Cube
187

Local Lfunctions The Archimedean Case
59
Global Lfunctions
65
Converse Theorems
73
Functoriality
81
Functoriality for the Classical Groups
87
Functoriality for the Classical Groups II
91
Automorphic Lfunctions
97
Chevalley Groups and their Properties
101
Cuspidal Representations
113
Lgroups and Automorphic Lfunctions
115
Induced Representations
119
Eisenstein Series and Constant Terms
129
Lfunctions in the Constant Terms
137
Meromorphic Continuation of Lfunctions
145
Generic Representations and their Whittaker Models
147
Functoriality of the Symmetric Fourth
193
Applications of Symmetric Power Lfunctions
203
The SatoTate Conjecture
207
Maass Wave Forms
213
The RankinSelberg Method
219
Oscillations of Fourier Coefficients of Cusp Forms
227
Poincaré Series
237
Kloosterman Sums and Selbergs Conjecture
243
Refined Estimates for Fourier Coefficients of Cusp Forms
247
Twisting and Averaging of Lserics
253
The KimSarnak Theorem
257
Introduction to Artin Lfunctions
265
Zeros and Poles of Artin Lfunctions
271
The LanglandsTunnell Theorem
275
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