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Explicit Formulas

for Regularized Products and Series

  • Book
  • © 1994

Overview

Authors:
  1. Jay Jorgenson
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  2. Serge Lang
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  3. Dorian Goldfeld
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1593)

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Table of contents (2 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Explicit formulas for regularized products and series

    • Jay Jorgenson, Serge Lang
    Pages 2-134

  3. A spectral interpretation of Weil's explicit formula

    • Dorian Goldfeld
    Pages 136-152

  4. Back Matter

    Pages 153-156
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Keywords

About this book

The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.

Bibliographic Information

  • Book Title: Explicit Formulas

  • Book Subtitle: for Regularized Products and Series

  • Authors: Jay Jorgenson, Serge Lang, Dorian Goldfeld

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0074039

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58673-9Published: 16 December 1994

  • eBook ISBN: 978-3-540-49041-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 160

  • Topics: Number Theory, Topological Groups, Lie Groups, Differential Geometry, Analysis

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