Lectures on Automorphic L-functions

by Cogdell, James W.; Kim, Henry H.; Murty, M. Ram

• ISBN13: 9780821848005
• ISBN10: 0821848003
• Format: Paperback
• Copyright: 2009-03-09
• Publisher: Amer Mathematical Society

Summary

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

Table of Contents

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

Table of Contents provided by Publisher. All Rights Reserved.