Automorphic forms on Adele groups

Author(s)

• Gelbart, Stephen S.

Bibliographic Information

Automorphic forms on Adele groups

by Stephen S. Gelbart

（Annals of mathematics studies, no. 83）

Princeton University Press, c1975

Note

Expanded from notes mimeographed at Cornell in May of 1972 and entitled Automorphic forms and representations of Adele groups

Bibliography: p. 260-263

Includes index

Description and Table of Contents

Description

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 Algebra

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BA01215902
• ISBN:
  • 0691081565
• LCCN: 74023388
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Princeton, N.J.
• Pages/Volumes: x, 267 p.
• Size: 24 cm
• Classification:
  • LCC : QA171
  • DC : 512/.22
• Subject Headings:
  • LCSH : Representations of groups
  • LCSH : Automorphic forms
  • LCSH : Linear algebraic groups
  • LCSH : Adeles
• Parent Bibliography ID:
  • BA00300336