Selberg Zeta Functions and Transfer Operators

An Experimental Approach to Singular Perturbations

  • Markus Szymon¬†Fraczek

Part of the Lecture Notes in Mathematics book series (LNM, volume 2139)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Markus Szymon Fraczek
    Pages 1-23
  3. Markus Szymon Fraczek
    Pages 25-37
  4. Markus Szymon Fraczek
    Pages 39-42
  5. Markus Szymon Fraczek
    Pages 43-68
  6. Markus Szymon Fraczek
    Pages 87-127
  7. Markus Szymon Fraczek
    Pages 297-300
  8. Back Matter
    Pages 301-354

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.


Character deformation Eigenvalues and resonances of hyperbolic Laplacian Selberg zeta function Singular perturbations of hyperbolic Laplacian Transfer operator method

Authors and affiliations

  • Markus Szymon¬†Fraczek
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUnited Kingdom

Bibliographic information