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Eisenstein Series and Automorphic Representations

2018-07-05 Mathematics
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Release : 2018-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 992/5 ( 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: This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.

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.

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.

Automorphic Forms, Automorphic Representations, and Arithmetic

1999
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Release : 1999
Genre :
Kind : eBook
Book Rating : 502/5 ( reviews)

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Book Synopsis Automorphic Forms, Automorphic Representations, and Arithmetic by : Robert S. Doran

Download or read book Automorphic Forms, Automorphic Representations, and Arithmetic written by Robert S. Doran. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt:

Eisenstein Series and Applications

2007-12-22 Mathematics
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Release : 2007-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 396/5 ( reviews)

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Book Synopsis Eisenstein Series and Applications by : Wee Teck Gan

Download or read book Eisenstein Series and Applications written by Wee Teck Gan. This book was released on 2007-12-22. Available in PDF, EPUB and Kindle. Book excerpt: Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.

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