TY  - BOOK
AU  - Fraczek,Markus Szymon
TI  - Selberg Zeta functions and transfer operators : : an experimental approach to singular perturbations 
T2  - Lecture notes in mathematics
SN  - 9783319512945 (alk. paper)
U1  - 515.56 23
PY  - 2017///
CY  - Cham
PB  - Springer
KW  - Zeta functions
KW  - Selberg trace formula.
KW  - Transfer operators.
N1  - Include index of notations and bibliographical references and index; 1. Introduction.-
2. Preliminaries.-
3. The Gamma function and the incomplete Gamma functions.-
4. The Hurwitz Zeta Function and the Lerch Zeta Function.-
5. Computation of the spectra and eigenvectors of large complex matrices.-
6. The hyperbolic Laplace-Beltrami operator.-
7. Transfer operators for the geodesic flow on hyperbolic surfaces.-
8. Numerical results for spectra and traces of the transfer operator for character deformations.-
9. Investigations of Selberg zeta functions under character deformations.-
10. Concluding remarks.-
Appendices.-
References.-
Index of Notations
N2  - 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
ER  -