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Author: Philipp Fleig
Publisher: Cambridge Studies in Advanced
Published: 2018-07-05
Total Pages: 587
ISBN-13: 1107189926
DOWNLOAD EBOOK →Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: Philipp Fleig
Publisher: Cambridge University Press
Published: 2018-07-05
Total Pages: 588
ISBN-13: 1108118992
DOWNLOAD EBOOK →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.
Author: Freydoon Shahidi
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 218
ISBN-13: 0821849891
DOWNLOAD EBOOK →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.
Author: Robert S. Doran
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 346
ISBN-13: 0821810510
DOWNLOAD EBOOK →Author: Colette Moeglin
Publisher: Cambridge University Press
Published: 1995-11-02
Total Pages: 382
ISBN-13: 9780521418935
DOWNLOAD EBOOK →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.
Author: S. Gelbart
Publisher: Springer
Published: 2013-12-01
Total Pages: 358
ISBN-13: 3662007347
DOWNLOAD EBOOK →International Colloquium an Automorphic Forms, Representation Theory and Arithmetic. Published for the Tata Institute of Fundamental Research, Bombay
Author: D. Bump
Publisher: Springer
Published: 2006-12-08
Total Pages: 196
ISBN-13: 3540390553
DOWNLOAD EBOOK →Author: Wee Teck Gan
Publisher: Springer Science & Business Media
Published: 2007-12-22
Total Pages: 317
ISBN-13: 0817646396
DOWNLOAD EBOOK →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.
Author: Robert S Doran Ze Li Dou George T Gilbert
Publisher: American Mathematical Soc.
Published: 1999-06-22
Total Pages: 348
ISBN-13: 9780821868416
DOWNLOAD EBOOK →Professor Goro Shimura was principal speaker at the conference on "Euler Products and Eisenstein Series" held at Texas Christian University (See CBMS Regional Conference Series in Mathematics, Volume 93). The present volume contains articles by leading specialists in the field. Some of these articles are based on talks given at the conference, whereas others were written purposely for this volume. The variety of the work presented reflects the current active state of the topic.
Author: H. Jacquet
Publisher: Springer
Published: 2006-11-15
Total Pages: 156
ISBN-13: 3540376127
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