Cohomological Theory of Dynamical Zeta Functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2001
|
| Series: | Progress in Mathematics
194 |
| Subjects: | |
| Links: | https://doi.org/10.1007/978-3-0348-8340-5 |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (X, 709 p) |
| ISBN: | 9783034883405 9783034895248 |
| DOI: | 10.1007/978-3-0348-8340-5 |
Staff View
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| 500 | |a 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 | ||
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| id | DE-604.BV042422104 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T13:02:22Z |
| institution | BVB |
| isbn | 9783034883405 9783034895248 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857521 |
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| physical | 1 Online-Ressource (X, 709 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Progress in Mathematics |
| spellingShingle | Juhl, Andreas Cohomological Theory of Dynamical Zeta Functions Mathematics Mathematics, general Mathematik Kohomologietheorie (DE-588)4164610-1 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4164610-1 (DE-588)4190764-4 |
| title | Cohomological Theory of Dynamical Zeta Functions |
| title_auth | Cohomological Theory of Dynamical Zeta Functions |
| title_exact_search | Cohomological Theory of Dynamical Zeta Functions |
| title_full | Cohomological Theory of Dynamical Zeta Functions by Andreas Juhl |
| title_fullStr | Cohomological Theory of Dynamical Zeta Functions by Andreas Juhl |
| title_full_unstemmed | Cohomological Theory of Dynamical Zeta Functions by Andreas Juhl |
| title_short | Cohomological Theory of Dynamical Zeta Functions |
| title_sort | cohomological theory of dynamical zeta functions |
| topic | Mathematics Mathematics, general Mathematik Kohomologietheorie (DE-588)4164610-1 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Kohomologietheorie Zetafunktion |
| url | https://doi.org/10.1007/978-3-0348-8340-5 |
| work_keys_str_mv | AT juhlandreas cohomologicaltheoryofdynamicalzetafunctions |