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＜電子ブック＞
Cohomological Theory of Dynamical Zeta Functions / by Andreas Juhl
(Progress in Mathematics. ISSN:2296505X ; 194)

版	1st ed. 2001.
出版者	Basel : Birkhäuser Basel : Imprint: Birkhäuser
出版年	2001
本文言語	英語
大きさ	X, 709 p : online resource
冊子体	Cohomological theory of dynamical zeta functions / Andreas Juhl
著者標目	*Juhl, Andreas author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-0348-8340-5

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