Progress in Mathematics

Cohomological Theory of Dynamical Zeta Functions

Authors: Juhl, Andreas

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About this book

Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo­ cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro­ jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-3-0348-8340-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
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Hardcover 176,79 €
price for Spain (gross)
  • ISBN 978-3-7643-6405-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-0348-9524-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Cohomological Theory of Dynamical Zeta Functions
Authors
Series Title
Progress in Mathematics
Series Volume
194
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag
eBook ISBN
978-3-0348-8340-5
DOI
10.1007/978-3-0348-8340-5
Hardcover ISBN
978-3-7643-6405-2
Softcover ISBN
978-3-0348-9524-8
Series ISSN
0743-1643
Edition Number
1
Number of Pages
X, 709
Topics