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Lecture Notes in Mathematics

An Approach to the Selberg Trace Formula via the Selberg Zeta-Function

Authors: Fischer, Jürgen

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The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $29.99
price for USA in USD
  • ISBN 978-3-540-39331-3
  • 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 in USD
  • ISBN 978-3-540-15208-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Approach to the Selberg Trace Formula via the Selberg Zeta-Function
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1253
Copyright
1987
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-39331-3
DOI
10.1007/BFb0077696
Softcover ISBN
978-3-540-15208-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IV, 188
Topics

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