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.
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.
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".
On Some Aspects Of The Theory Of Anosov Systems
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Author : Grigorii A. Margulis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
On Some Aspects Of The Theory Of Anosov Systems written by Grigorii A. Margulis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.
Fractal Geometry Complex Dimensions And Zeta Functions
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Author : Michel L. Lapidus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-08
Fractal Geometry Complex Dimensions And Zeta Functions written by Michel L. Lapidus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-08 with Mathematics categories.
Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.
Number Fields And Function Fields Two Parallel Worlds
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Author : Gerard van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-14
Number Fields And Function Fields Two Parallel Worlds written by Gerard van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-14 with Mathematics categories.
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections
A Tribute To C S Seshadri
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Author : Venkatrama Lakshmibai
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-24
A Tribute To C S Seshadri written by Venkatrama Lakshmibai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-24 with Mathematics categories.
C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.
Categorical Decomposition Techniques In Algebraic Topology
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Author : Gregory Arone
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-27
Categorical Decomposition Techniques In Algebraic Topology written by Gregory Arone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-27 with Mathematics categories.
The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".
Spectral Problems In Geometry And Arithmetic
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Author : Thomas Branson
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Spectral Problems In Geometry And Arithmetic written by Thomas Branson 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 1999 with Mathematics categories.
These are the proceedings of the NSF-CBMS Conference on "Spectral Problems in Geometry and Arithmetic" held at the University of Iowa. The principal speaker was Peter Sarnak, who has been a central contributor to developments in this field. The volume approaches the topic from the geometric, physical, and number theoretic points of view. The remarkable new connections among seemingly disparate mathematical and scientific disciplines have surprised even veterans of the physical mathematics renaissance forged by gauge theory in the 1970s. Numerical experiments show that the local spacing between zeros of the Riemann zeta function is modelled by spectral phenomena: the eigenvalue distributions of random matrix theory, in particular the Gaussian unitary ensemble (GUE). Related phenomena are from the point of view of differential geometry and global harmonic analysis. Elliptic operators on manifolds have (through zeta function regularization) functional determinants, which are related to functional integrals in quantum theory. The search for critical points of this determinant brings about extremely subtle and delicate sharp inequalities of exponential type. This indicates that zeta functions are spectral objects-and even physical objects. This volume demonstrates that zeta functions are also dynamic, chaotic, and more.