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The Selberg-Arthur Trace Formula

Based on Lectures by James Arthur

  • Book
  • © 1992
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Overview

Authors:
  1. Salahoddin Shokranian
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1503)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VII
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  2. Number theory and automorphic representations

    • Salahoddin Shokranian
    Pages 1-10
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  3. Selberg's trace formula

    • Salahoddin Shokranian
    Pages 11-23
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  4. Kernel functions and the convergence theorem

    • Salahoddin Shokranian
    Pages 24-40
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  5. The adèlic theory

    • Salahoddin Shokranian
    Pages 41-44
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  6. The geometric theory

    • Salahoddin Shokranian
    Pages 45-59
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  7. The geometric expansion of the trace formula

    • Salahoddin Shokranian
    Pages 60-68
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  8. The spectral theory

    • Salahoddin Shokranian
    Pages 69-78
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  9. The invariant trace formula and its applications

    • Salahoddin Shokranian
    Pages 79-86
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  10. Back Matter

    Pages 87-97
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Keywords

About this book

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

Bibliographic Information

  • Book Title: The Selberg-Arthur Trace Formula

  • Book Subtitle: Based on Lectures by James Arthur

  • Authors: Salahoddin Shokranian

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0092305

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Softcover ISBN: 978-3-540-55021-1Published: 12 February 1992

  • eBook ISBN: 978-3-540-46659-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 99

  • Topics: Number Theory, Topological Groups, Lie Groups

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