Cohomological Theory Of Dynamical Zeta Functions
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Cohomological Theory Of Dynamical Zeta Functions
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Author : Andreas Juhl
language : en
Publisher:
Release Date : 2000-12-01
Cohomological Theory Of Dynamical Zeta Functions written by Andreas Juhl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-01 with categories.
Cohomological Theory Of Dynamical Zeta Functions
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Author : Andreas Juhl
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Cohomological Theory Of Dynamical Zeta Functions written by Andreas Juhl and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion
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Author : Alexander Fel'shtyn
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion written by Alexander Fel'shtyn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Fixed point theory categories.
In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Dynamical Zeta Functions For Piecewise Monotone Maps Of The Interval
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Author : David Ruelle
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Dynamical Zeta Functions For Piecewise Monotone Maps Of The Interval written by David Ruelle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
With a general introduction to the subject, this title presents a detailed study of the zeta functions associated with piecewise monotone maps of the interval $ 0,1]$. In particular, it gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of $\zeta (z)$ and the eigenvalues of the transfer operator.
Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion
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Author : Alexander L. Fel'shtyn
language : en
Publisher:
Release Date : 1992
Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion written by Alexander L. Fel'shtyn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Selberg Zeta Functions And Transfer Operators
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Author : Markus Szymon Fraczek
language : en
Publisher: Springer
Release Date : 2017-05-11
Selberg Zeta Functions And Transfer Operators written by Markus Szymon Fraczek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-11 with Mathematics categories.
This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.
Algebraic Groups
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Author : Yuri Tschinkel
language : en
Publisher: Universitätsverlag Göttingen
Release Date : 2007
Algebraic Groups written by Yuri Tschinkel and has been published by Universitätsverlag Göttingen this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algebraic varieties categories.
Contributions To The Theory Of Zeta Functions
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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2015
Contributions To The Theory Of Zeta Functions written by Shigeru Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
Mathematical Works
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Author : Erich Kähler
language : en
Publisher: Walter de Gruyter
Release Date : 2003
Mathematical Works written by Erich Kähler and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".
Selberg Zeta And Theta Functions
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Author : Ulrich Bunke
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1995
Selberg Zeta And Theta Functions written by Ulrich Bunke and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The authors give a self contained exposition of the theory of Selberg zeta and theta functions for bundles on compact locally symmetric spaces of rank 1. The connection between these functions and the spectrum of certain elliptic differential operators is provided by a version of the Selberg trace formula. The theta function is a regularized trace of the wave group. Originally defined geometrically, the Selberg zeta function has a representation in terms of regularized determinants. This leads to a complete description of its singularities. These results are employed in order to establish a functional equation and further properties of the Ruelle zeta function. A couple of explicit examples is worked out. Additional chapters are devoted to the theta function of Riemannian surfaces with cusps and to alternative descriptions of the singularities of the Selberg zeta function in terms of Lie algebra and group cohomology.