1.

Record Nr.

UNISA996466642003316

Autore

Fraczek Markus Szymon

Titolo

Selberg Zeta Functions and Transfer Operators [[electronic resource] ] : An Experimental Approach to Singular Perturbations / / by Markus Szymon Fraczek

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

ISBN

3-319-51296-X

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (XV, 354 p. 71 illus., 43 illus. in color.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2139

Disciplina

515.56

Soggetti

Number theory

Computer mathematics

Approximation theory

Functions of complex variables

Special functions

Dynamics

Ergodic theory

Number Theory

Computational Mathematics and Numerical Analysis

Approximations and Expansions

Functions of a Complex Variable

Special Functions

Dynamical Systems and Ergodic Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Sommario/riassunto

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.