Explicit Formulas for Regularized Products and Series

  • Authors
  • Jay Jorgenson
  • Serge Lang
  • Dorian Goldfeld
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1593)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Jay Jorgenson, Serge Lang
    Pages 2-134
  3. Back Matter
    Pages 153-156

About this book

Introduction

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.

Keywords

Analytic number theory Spectral theory Zeta-functions manifold number theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0074039
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58673-9
  • Online ISBN 978-3-540-49041-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book