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

Stephen S. Gelbart

Published by Princeton University Press 1975

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

Stephen S. Gelbart

Volume 83 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400881611

Overview
Contents

About this book

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?

Topics

Frontmatter Publicly Available Download PDF	i
PREFACE Requires Authentication Unlicensed Licensed Download PDF	vii
CONTENTS Publicly Available Download PDF	ix
§1. THE CLASSICAL THEORY Requires Authentication Unlicensed Licensed Download PDF	1
§2. AUTOMORPHIC FORMS AND THE DECOMPOSITION OF L²(Γ\SL(2,ℝ)) Requires Authentication Unlicensed Licensed Download PDF	22
§3. AUTOMORPHIC FORMS AS FUNCTIONS ON THE ADELE GROUP OF GL(2) Requires Authentication Unlicensed Licensed Download PDF	40
§4. THE REPRESENTATIONS OF GL(2) OVER LOCAL AND GLOBAL FIELDS Requires Authentication Unlicensed Licensed Download PDF	54
§5 . CUSP FORMS AND REPRESENTATIONS OF THE ADELE GROUP OF GL(2) Requires Authentication Unlicensed Licensed Download PDF	79
§6. HECKE THEORY FOR GL(2) Requires Authentication Unlicensed Licensed Download PDF	98
§7 . THE CONSTRUCTION OF A SPECIAL CLASS OF AUTOMORPHIC FORMS Requires Authentication Unlicensed Licensed Download PDF	133
§ 8 . EISENSTEIN SERIES AND THE CONTINUOUS SPECTRUM Requires Authentication Unlicensed Licensed Download PDF	161
§9. THE TRACE FORMULA FOR GL(2) Requires Authentication Unlicensed Licensed Download PDF	181
§10. AUTOMORPHIC FORMS ON A QUATERNION ALGEBRA Requires Authentication Unlicensed Licensed Download PDF	227
BIBLIOGRAPHY Requires Authentication Unlicensed Licensed Download PDF	260
INDEX Requires Authentication Unlicensed Licensed Download PDF	264