Automorphic Forms on Adele Groups. (AM-83), Volume 83
Automorphic Forms on Adele Groups. (AM-83), Volume 83

Author: Stephen S. Gelbart

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 280

ISBN-13: 1400881617

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This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Automorphic Forms on Adele Groups
Automorphic Forms on Adele Groups

Author: Stephen S. Gelbart

Publisher: Princeton University Press

Published: 1975-03-21

Total Pages: 0

ISBN-13: 9780691081564

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This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Automorphic Forms and L-Functions for the Group GL(n,R)
Automorphic Forms and L-Functions for the Group GL(n,R)

Author: Dorian Goldfeld

Publisher: Cambridge University Press

Published: 2006-08-03

Total Pages: 65

ISBN-13: 1139456202

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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.

Topological Automorphic Forms
Topological Automorphic Forms

Author: Mark Behrens

Publisher: American Mathematical Soc.

Published: 2010-02-22

Total Pages: 167

ISBN-13: 082184539X

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The authors apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type $U(1,n-1)$. These cohomology theories of topological automorphic forms ($\mathit{TAF}$) are related to Shimura varieties in the same way that $\mathit{TMF}$ is related to the moduli space of elliptic curves.

Eisenstein Series and Automorphic Representations
Eisenstein Series and Automorphic Representations

Author: Philipp Fleig

Publisher: Cambridge Studies in Advanced

Published: 2018-07-05

Total Pages: 587

ISBN-13: 1107189926

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

Modern Analysis of Automorphic Forms By Example
Modern Analysis of Automorphic Forms By Example

Author: Paul Garrett

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 407

ISBN-13: 1107154006

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Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

An Introduction to the Langlands Program
An Introduction to the Langlands Program

Author: Joseph Bernstein

Publisher: Springer Science & Business Media

Published: 2013-12-11

Total Pages: 283

ISBN-13: 0817682260

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This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.