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.
