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- catalog abstract ""The periodic orbits of the geodesic flow of compact locally symmetric spaces of negative curvature give rise to meromorphic zeta functions (generalized Selberg zeta functions, Ruelle zeta functions). The book treats various aspects of the idea to understand the analytical properties of these zeta functions on the basis of appropriate analogs of the Lefschetz fixed point formula in which the periodic orbits of the flow take the place of the fixed points. According to geometric quantization the Anosov foliations of the sphere bundle provide a natural source for the definition of the cohomological data in the Lefschetz formula. The Lefschetz formula method can be considered as a link between the automorphic approach (Selberg trace formula) and Ruelle's approach (transfer operators). It yields a uniform cohomological characterization of the zeros and poles of the zeta functions and a new understanding of the functional equations from an index theoretical point of view. The divisors of the Selberg zeta functions also admit characterizations in terms of harmonic currents on the sphere bundle which represent the cohomology classes in the Lefschetz formulas in the sense of a Hodge theory. The concept of harmonic currents to be used for that purpose is introduced here for the first time. Harmonic currents for the geodesic flow of a non-compact hyperbolic space with a compact convex core generalize the Patterson-Sullivan measure on the limit set and are responsible for the zeros and poles of the corresponding zeta function." "The book should be appealing not only to the specialists on zeta functions which will find their object of favorite interest connected in new ways with index theory, geometric quantization methods, foliation theory and representation theory."--Jacket.".
- catalog contributor b12021099.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description ""The periodic orbits of the geodesic flow of compact locally symmetric spaces of negative curvature give rise to meromorphic zeta functions (generalized Selberg zeta functions, Ruelle zeta functions). The book treats various aspects of the idea to understand the analytical properties of these zeta functions on the basis of appropriate analogs of the Lefschetz fixed point formula in which the periodic orbits of the flow take the place of the fixed points. According to geometric quantization the Anosov foliations of the sphere bundle provide a natural source for the definition of the cohomological data in the Lefschetz formula.".
- catalog description "Harmonic currents for the geodesic flow of a non-compact hyperbolic space with a compact convex core generalize the Patterson-Sullivan measure on the limit set and are responsible for the zeros and poles of the corresponding zeta function." "The book should be appealing not only to the specialists on zeta functions which will find their object of favorite interest connected in new ways with index theory, geometric quantization methods, foliation theory and representation theory."--Jacket.".
- catalog description "Includes bibliographical references (p. [687]-701) and indexes.".
- catalog description "The Lefschetz formula method can be considered as a link between the automorphic approach (Selberg trace formula) and Ruelle's approach (transfer operators). It yields a uniform cohomological characterization of the zeros and poles of the zeta functions and a new understanding of the functional equations from an index theoretical point of view. The divisors of the Selberg zeta functions also admit characterizations in terms of harmonic currents on the sphere bundle which represent the cohomology classes in the Lefschetz formulas in the sense of a Hodge theory. The concept of harmonic currents to be used for that purpose is introduced here for the first time.".
- catalog description "Zeta functions of the geodesic flow of compact locally symmetric manifolds -- Operators and complexes -- Verma complexes on SY and SX -- Harmonic currents and canonical complexes -- Divisors and harmonic currents -- Further developments and open problems.".
- catalog extent "x, 709 p. ;".
- catalog identifier "376436405X (Birkhäuser : acid-free paper)".
- catalog isPartOf "Progress in mathematics (Boston, Mass.) ; v. 194.".
- catalog isPartOf "Progress in mathematics ; v. 194".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "Basel ; Boston : Birkhäuser,".
- catalog subject "515/.56 21".
- catalog subject "Functions, Zeta.".
- catalog subject "Homology theory.".
- catalog subject "QA351 .J84 2001".
- catalog tableOfContents "Zeta functions of the geodesic flow of compact locally symmetric manifolds -- Operators and complexes -- Verma complexes on SY and SX -- Harmonic currents and canonical complexes -- Divisors and harmonic currents -- Further developments and open problems.".
- catalog title "Cohomological theory of dynamical zeta functions / Andreas Juhl.".
- catalog type "text".