Overview
- The only book on the market which describes the evaluation of Selberg zeta functions for character deformations via the transfer operator method
- Gives a detailed description of numerical methods and analytic theories in one book
- Provides animations and over 50 color illustrations, helping the reader to get a better understanding
- Gives numerical and analytical results on new phenomena related to singular perturbations of hyperbolic Laplacians
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2139)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“What makes this book a unique is that it systematically covers effective computation of the spectral terms of the selberg trace formula, namely the eigenvectors, eigenfunctions and resonances. ... The computation of this book gives us a hint as to what actually occurs with the extremely complicated limit … The book is self-contained, covering both the theoretical background and the numerical aspects.” (Joshua S. Friedman, Mathematical Reviews, May, 2018)
Authors and Affiliations
Bibliographic Information
Book Title: Selberg Zeta Functions and Transfer Operators
Book Subtitle: An Experimental Approach to Singular Perturbations
Authors: Markus Szymon Fraczek
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-51296-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-51294-5Published: 14 May 2017
eBook ISBN: 978-3-319-51296-9Published: 11 May 2017
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XV, 354
Number of Illustrations: 28 b/w illustrations, 43 illustrations in colour
Topics: Number Theory, Computational Mathematics and Numerical Analysis, Approximations and Expansions, Functions of a Complex Variable, Special Functions, Dynamical Systems and Ergodic Theory