Selberg Zeta Functions And Transfer Operators

Author : Markus Szymon Fraczek
Publisher : Springer
ISBN 13 : 331951296X
Total Pages : 363 pages
Book Rating : 4.69/5 ( download)

DOWNLOAD NOW!

Download or read book Selberg Zeta Functions and Transfer Operators written by Markus Szymon Fraczek and published by Springer. This book was released on 2017-05-11 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author :
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.84/5 ( download)

DOWNLOAD NOW!

Download or read book Selberg Zeta Functions and Transfer Operators for Modular Groups written by and published by . This book was released on 2004 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ulrich Bunke
Publisher : De Gruyter Akademie Forschung
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.16/5 ( download)

DOWNLOAD NOW!

Download or read book Selberg Zeta and Theta Functions written by Ulrich Bunke and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 0821820796
Total Pages : 210 pages
Book Rating : 4.97/5 ( download)

DOWNLOAD NOW!

Download or read book Dynamical, Spectral, and Arithmetic Zeta Functions written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2001 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.

Author : Markus Szymon Fraczek
Publisher :
ISBN 13 : 9783943917406
Total Pages : 210 pages
Book Rating : 4.01/5 ( download)

DOWNLOAD NOW!

Download or read book Character Deformation of the Selberg Zeta Function for Congruence Subgroups Via the Transfer Operator written by Markus Szymon Fraczek and published by . This book was released on 2012 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Andreas Juhl
Publisher : Birkhäuser
ISBN 13 : 3034883404
Total Pages : 712 pages
Book Rating : 4.05/5 ( download)

DOWNLOAD NOW!

Download or read book Cohomological Theory of Dynamical Zeta Functions written by Andreas Juhl and published by Birkhäuser. This book was released on 2012-12-06 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kurokawa N. (Nobushige)
Publisher :
ISBN 13 :
Total Pages : 466 pages
Book Rating : 4.73/5 ( download)

DOWNLOAD NOW!

Download or read book Zeta Functions in Geometry written by Kurokawa N. (Nobushige) and published by . This book was released on 1992 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains accounts of work presented during the research conference, ``Zeta Functions in Geometry,'' held at the Tokyo Institute of Technology in August 1990. The aim of the conference was to provide an opportunity for the discussion of recent results by geometers and number theorists on zeta functions in several different categories. The exchange of ideas produced new insights on various geometric zeta functions, as well as the classical zeta functions. The zeta functions covered here are the Selberg zeta functions, the Ihara zeta functions, spectral zeta functions, and those associated with prehomogeneous vector spaces. Accessible to graduate students with background in geometry and number theory, Zeta Functions in Geometry will prove useful for its presentation of new results and up-to-date surveys.

Author : Roelof Bruggeman
Publisher : American Mathematical Society
ISBN 13 : 1470465450
Total Pages : 186 pages
Book Rating : 4.52/5 ( download)

DOWNLOAD NOW!

Download or read book Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume written by Roelof Bruggeman and published by American Mathematical Society. This book was released on 2023-07-31 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Shin-y Koyama
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.23/5 ( download)

DOWNLOAD NOW!

Download or read book Selberg Zeta Functions and Ruelle Operators for Function Fields written by Shin-y Koyama and published by . This book was released on 1991 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sergiǐ Kolyada:
Publisher : American Mathematical Soc.
ISBN 13 : 1470420201
Total Pages : 330 pages
Book Rating : 4.08/5 ( download)

DOWNLOAD NOW!

Download or read book Dynamics and Numbers written by Sergiǐ Kolyada: and published by American Mathematical Soc.. This book was released on 2016-07-27 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.