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Eisenstein Series and Automorphic $L$-Functions

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 891/5 ( reviews)

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Book Synopsis Eisenstein Series and Automorphic $L$-Functions by : Freydoon Shahidi

Download or read book Eisenstein Series and Automorphic $L$-Functions written by Freydoon Shahidi. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: 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

2018-07-05 Mathematics
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Release : 2018-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 926/5 ( reviews)

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Book Synopsis Eisenstein Series and Automorphic Representations by : Philipp Fleig

Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig. This book was released on 2018-07-05. Available in PDF, EPUB and Kindle. Book excerpt: Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Analytic Properties of Automorphic L-Functions

2014-07-14 Mathematics
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Release : 2014-07-14
Genre : Mathematics
Kind : eBook
Book Rating : 034/5 ( reviews)

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Book Synopsis Analytic Properties of Automorphic L-Functions by : Stephen Gelbart

Download or read book Analytic Properties of Automorphic L-Functions written by Stephen Gelbart. This book was released on 2014-07-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Decomposition and Eisenstein Series

1995-11-02 Mathematics
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Release : 1995-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 935/5 ( reviews)

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Book Synopsis Spectral Decomposition and Eisenstein Series by : Colette Moeglin

Download or read book Spectral Decomposition and Eisenstein Series written by Colette Moeglin. This book was released on 1995-11-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Explicit Constructions of Automorphic L-Functions

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 809/5 ( reviews)

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Book Synopsis Explicit Constructions of Automorphic L-Functions by : Stephen Gelbart

Download or read book Explicit Constructions of Automorphic L-Functions written by Stephen Gelbart. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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