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Cohomological Theory of Dynamical Zeta Functions

Cohomological Theory of Dynamical Zeta Functions
Catalogue Information
Field name Details
Dewey Class 515
Title Cohomological Theory of Dynamical Zeta Functions ([EBook] /) / by Andreas Juhl.
Author Juhl, Andreas
Other name(s) SpringerLink (Online service)
Publication Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2001.
Physical Details X, 709 p. : online resource.
Series Progress in mathematics 0743-1643 ; ; 194
ISBN 9783034883405
Summary Note 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.:
Contents note 1. Introduction -- 2. Preliminaries -- 3. Zeta Functions of the Geodesic Flow of Compact Locally Symmetric Manifolds -- 4. Operators and Complexes -- 5. The Verma Complexes on SY and SX -- 6. Harmonic Currents and Canonical Complexes -- 7. Divisors and Harmonic Currents -- 8. Further Developments and Open Problems -- 9. A Summary of Important Formulas -- Index of Equations.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-3-0348-8340-5
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