Eisenstein Series And Automorphic L Functions

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Eisenstein Series And Automorphic L Functions

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Author : Freydoon Shahidi
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-07

Eisenstein Series And Automorphic L Functions written by Freydoon Shahidi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-07 with Mathematics categories.

This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands–Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman–Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.

Eisenstein Series And Automorphic Representations

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Author : Philipp Fleig
language : en
Publisher: Cambridge Studies in Advanced
Release Date : 2018-07-05

Eisenstein Series And Automorphic Representations written by Philipp Fleig and has been published by Cambridge Studies in Advanced this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.

Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Explicit Constructions Of Automorphic L Functions

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Author : Stephen Gelbart
language : en
Publisher: Springer
Release Date : 2006-11-15

Explicit Constructions Of Automorphic L Functions written by Stephen Gelbart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.

Spectral Decomposition And Eisenstein Series

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Author : Colette Moeglin
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-02

Spectral Decomposition And Eisenstein Series written by Colette Moeglin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-02 with Mathematics categories.

A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.

Analytic Properties Of Automorphic L Functions

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Author : Stephen Gelbart
language : en
Publisher: Academic Press
Release Date : 2014-07-14

Analytic Properties Of Automorphic L Functions written by Stephen Gelbart and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.

Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products . This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.

Lectures On Automorphic L Functions

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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date :

Lectures On Automorphic L Functions written by James W. Cogdell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

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

Automorphic Forms And L Functions For The Group Gl N R

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Author : Dorian Goldfeld
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-26

Automorphic Forms And L Functions For The Group Gl N R written by Dorian Goldfeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Mathematics categories.

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.

Eisenstein Series And Rationality Of Automorphic L Functions On Anisotropic Unitary Groups Over Function Fields

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Author : Lu Zheng
language : en
Publisher:
Release Date : 1993

Eisenstein Series And Rationality Of Automorphic L Functions On Anisotropic Unitary Groups Over Function Fields written by Lu Zheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Lectures On Automorphic L Functions

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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Lectures On Automorphic L Functions written by James W. Cogdell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This book provides a comprehensive account of the crucial role automorphic $L$-functions play in number theory and in the Langlands program, especially the Langlands functoriality conjecture. There has been a recent major development in the Langlands functoriality conjecture by the use of automorphic $L$-functions, namely, by combining converse theorems of Cogdell and Piatetski-Shapiro with the Langlands-Shahidi method. This book provides a step-by-step introduction to these developments and explains how the Langlands functoriality conjecture implies solutions to several outstanding conjectures in number theory, such as the Ramanujan conjecture, Sato-Tate conjecture, and Artin's conjecture. It would be ideal for an introductory course in the Langlands program. Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). 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. This is a reprint of the 2004 original. (FIM/20.S)