The Selberg-Arthur Trace Formula

Based on Lectures by James Arthur

  • Authors
  • Salahoddin Shokranian

Part of the Lecture Notes in Mathematics book series (LNM, volume 1503)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Salahoddin Shokranian
    Pages 1-10
  3. Salahoddin Shokranian
    Pages 11-23
  4. Salahoddin Shokranian
    Pages 24-40
  5. Salahoddin Shokranian
    Pages 41-44
  6. Salahoddin Shokranian
    Pages 45-59
  7. Salahoddin Shokranian
    Pages 60-68
  8. Salahoddin Shokranian
    Pages 69-78
  9. Salahoddin Shokranian
    Pages 79-86
  10. Back Matter
    Pages 87-97

About this book

Introduction

This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks

Keywords

Invariant automorphic forms calculus function harmonic analysis number theory theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092305
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55021-1
  • Online ISBN 978-3-540-46659-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book