Lecture Notes in Mathematics

Explicit Formulas

for Regularized Products and Series

Authors: Jorgenson, Jay, Lang, Serge, Goldfeld, Dorian

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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.

Table of contents (2 chapters)

  • Explicit formulas for regularized products and series

    Jorgenson, Jay (et al.)

    Pages 2-134

  • A spectral interpretation of Weil's explicit formula

    Goldfeld, Dorian

    Pages 136-152

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-49041-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-3-540-58673-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Explicit Formulas
Book Subtitle
for Regularized Products and Series
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1593
Copyright
1994
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-49041-8
DOI
10.1007/BFb0074039
Softcover ISBN
978-3-540-58673-9
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 160
Topics