Automorphic Forms on Adele Groups. (AM-83), Volume 83 / Stephen S. Gelbart.

Format:

Book

Author/Creator:

Gelbart, Stephen S., author.

Series:

Annals of mathematics studies ; Number 83.

Annals of Mathematics Studies ; 262

Language:

English

Subjects (All):

Representations of groups.

Automorphic forms.

Linear algebraic groups.

Adeles.

Physical Description:

1 online resource (280 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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?

Contents:

Frontmatter

PREFACE

CONTENTS

§1. THE CLASSICAL THEORY

§2. AUTOMORPHIC FORMS AND THE DECOMPOSITION OF L2(ΓSL(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 ALGEBRA

BIBLIOGRAPHY

INDEX

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881611

1400881617

OCLC:

979968791