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Cohomological Theory of Dynamical Zeta Functions

  • Book
  • © 2001

Overview

Authors:
  1. Andreas Juhl

    1. Matematiska Institutionen, Universitet Uppsala, Uppsala

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Part of the book series: Progress in Mathematics (PM, volume 194)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Andreas Juhl
    Pages 1-61

  3. Preliminaries

    • Andreas Juhl
    Pages 63-85

  4. Zeta Functions of the Geodesic Flow of Compact Locally Symmetric Manifolds

    • Andreas Juhl
    Pages 87-230

  5. Operators and Complexes

    • Andreas Juhl
    Pages 231-329

  6. The Verma Complexes on SY and SX

    • Andreas Juhl
    Pages 331-372

  7. Harmonic Currents and Canonical Complexes

    • Andreas Juhl
    Pages 373-468

  8. Divisors and Harmonic Currents

    • Andreas Juhl
    Pages 469-518

  9. Further Developments and Open Problems

    • Andreas Juhl
    Pages 519-671

  10. A Summary of Important Formulas

    • Andreas Juhl
    Pages 673-685

  11. Back Matter

    Pages 687-709
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Keywords

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.

Authors and Affiliations

  • Matematiska Institutionen, Universitet Uppsala, Uppsala

    Andreas Juhl

Bibliographic Information

  • Book Title: Cohomological Theory of Dynamical Zeta Functions

  • Authors: Andreas Juhl

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8340-5

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 2001

  • Hardcover ISBN: 978-3-7643-6405-2Published: 01 December 2000

  • Softcover ISBN: 978-3-0348-9524-8Published: 23 October 2012

  • eBook ISBN: 978-3-0348-8340-5Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: X, 709

  • Topics: Analysis

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