Selberg Zeta Functions And Transfer Operators

Author : Markus Szymon Fraczek
Publisher : Springer
Page : 354 pages
File Size : 46,5 Mb
Release : 2017-05-11
Category : Mathematics
ISBN : 9783319512969

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Selberg Zeta Functions and Transfer Operators by Markus Szymon Fraczek Pdf

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 : Ulrich Bunke,Martin Olbrich
Publisher : De Gruyter Akademie Forschung
Page : 176 pages
File Size : 42,6 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015037446716

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Selberg Zeta and Theta Functions by Ulrich Bunke,Martin Olbrich Pdf

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 : Markus Szymon Fraczek
Publisher : Unknown
Page : 210 pages
File Size : 43,9 Mb
Release : 2012
Category : Electronic
ISBN : 3943917401

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Character Deformation of the Selberg Zeta Function for Congruence Subgroups Via the Transfer Operator by Markus Szymon Fraczek Pdf

Author : Michel Laurent Lapidus,Spectral AMS Special Session on Dynamical,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 48,6 Mb
Release : 2001
Category : Functions, Zeta
ISBN : 9780821820797

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Dynamical, Spectral, and Arithmetic Zeta Functions by Michel Laurent Lapidus,Spectral AMS Special Session on Dynamical,Machiel Van Frankenhuysen Pdf

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 : Roelof Bruggeman,Anke Dorothea Pohl
Publisher : American Mathematical Society
Page : 186 pages
File Size : 48,5 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781470465452

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Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume by Roelof Bruggeman,Anke Dorothea Pohl Pdf

View the abstract.

Author : Andreas Juhl
Publisher : Birkhäuser
Page : 712 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883405

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Cohomological Theory of Dynamical Zeta Functions by Andreas Juhl Pdf

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 : Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 45,8 Mb
Release : 2016-07-27
Category : Ergodic theory
ISBN : 9781470420208

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Dynamics and Numbers by Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward Pdf

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.

Author : Jens Bölte,Frank Steiner
Publisher : Cambridge University Press
Page : 285 pages
File Size : 50,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9781107610491

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Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology by Jens Bölte,Frank Steiner Pdf

Leading experts introduce this classical subject with exciting new applications in theoretical physics.

Author : Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko
Publisher : Springer Science & Business Media
Page : 693 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215448

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Emerging Applications of Number Theory by Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko Pdf

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Author : Bernold Fiedler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642565892

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Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by Bernold Fiedler Pdf

Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Author : R. Bruggeman,J. Lewis,D. Zagier
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 49,5 Mb
Release : 2015-08-21
Category : Algebraic topology
ISBN : 9781470414078

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Period Functions for Maass Wave Forms and Cohomology by R. Bruggeman,J. Lewis,D. Zagier Pdf

The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.

Author : S. F. Koli͡ada,Thomas Ward
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 46,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837511

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Algebraic and Topological Dynamics by S. F. Koli͡ada,Thomas Ward Pdf

This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statistical properties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.

Author : Tobias Mühlenbruch,Wissam Raji
Publisher : Springer Nature
Page : 527 pages
File Size : 46,5 Mb
Release : 2020-05-06
Category : Mathematics
ISBN : 9783030404758

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On the Theory of Maass Wave Forms by Tobias Mühlenbruch,Wissam Raji Pdf

This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of research are explored in depth, such as Maass wave forms of real weight and the cohomology attached to Maass wave forms and transfer operators. Because Maass wave forms are given a deep exploration, this book offers an indispensable resource for those entering the field. Early chapters present a brief introduction to the theory of classical modular forms, with an emphasis on objects and results necessary to fully understand later material. Chapters 4 and 5 contain the book’s main focus: L-functions and period functions associated with families of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms. Engaging exercises appear throughout the book, with solutions available online. On the Theory of Maass Wave Forms is ideal for graduate students and researchers entering the area. Readers in mathematical physics and other related disciplines will find this a useful reference as well. Knowledge of complex analysis, real analysis, and abstract algebra is required.

Author : G Gyorgyi,I Kondor,L Sasvari,Tamas Tel
Publisher : World Scientific
Page : 600 pages
File Size : 41,7 Mb
Release : 1992-04-29
Category : Science
ISBN : 9789814505659

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From Phase Transitions To Chaos: Topics In Modern Statistical Physics by G Gyorgyi,I Kondor,L Sasvari,Tamas Tel Pdf

This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Péter Szépfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.

Author : Anonim
Publisher : ScholarlyEditions
Page : 700 pages
File Size : 48,7 Mb
Release : 2013-06-20
Category : Mathematics
ISBN : 9781490105826

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Issues in Algebra, Geometry, and Topology: 2013 Edition by Anonim Pdf

Issues in Algebra, Geometry, and Topology / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Topology in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.