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Lecture Notes in Mathematics

Selberg Zeta Functions and Transfer Operators

An Experimental Approach to Singular Perturbations

Authors: Fraczek, Markus Szymon

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  • 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
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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-51296-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-51294-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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)

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-51296-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-51294-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Selberg Zeta Functions and Transfer Operators
Book Subtitle
An Experimental Approach to Singular Perturbations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2139
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-51296-9
DOI
10.1007/978-3-319-51296-9
Softcover ISBN
978-3-319-51294-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XV, 354
Number of Illustrations
28 b/w illustrations, 43 illustrations in colour
Topics