Eisenstein Series And Automorphic Representations
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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.
Automorphic Forms Automorphic Representations And Arithmetic
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Automorphic Forms Automorphic Representations And Arithmetic written by Robert S. Doran 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 1999 with categories.
Eisenstein Series And Automorphic L Functions
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Author : Freydoon Shahidi
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Eisenstein Series And Automorphic L Functions written by Freydoon Shahidi 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 2010 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 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.
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.
The Descent Map From Automorphic Representations Of Gl N To Classical Groups
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Author : David Soudry
language : en
Publisher: World Scientific
Release Date : 2011-06-30
The Descent Map From Automorphic Representations Of Gl N To Classical Groups written by David Soudry and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-30 with Mathematics categories.
This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.
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.
An Introduction To Automorphic Representations
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Author : Jayce R. Getz
language : en
Publisher: Springer Nature
Release Date : 2024-03-01
An Introduction To Automorphic Representations written by Jayce R. Getz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-01 with Mathematics categories.
The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics. The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed. This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface.
Spectral Methods Of Automorphic Forms
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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Spectral Methods Of Automorphic Forms written by Henryk Iwaniec 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 2002 with Mathematics categories.
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this volume was an underground classic, both as a textbook and as a respected source for results, ideas, and references. The book's reputation sparked a growing interest inthe mathematical community to bring it back into print. The AMS has answered that call with the publication of this second edition. In the book, Iwaniec treats the spectral theory of automorphic forms as the study of the space $L2 (H\Gamma)$, where $H$ is the upper half-plane and $\Gamma$ is a discretesubgroup of volume-preserving transformations of $H$. He combines various techniques from analytic number theory. Among the topics discussed are Eisenstein series, estimates for Fourier coefficients of automorphic forms, the theory of Kloosterman sums, the Selberg trace formula, and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 AMS Cole Prize for his fundamental contributions to analytic number theory. Also available from the AMS by H. Iwaniec is Topics in ClassicalAutomorphic Forms, Volume 17 in the Graduate Studies in Mathematics series. The book is designed for graduate students and researchers working in analytic number theory.