Markus Fraczek
Email: markus.fraczek at gmail.com
Books
Selberg Zeta Functions and Transfer Operators , An Experimental Approach to Singular Perturbations, M. Fraczek, Lecture Notes in Mathematics 2139 Springer (2017), Springer website
Research Interests
Selberg zeta functions for congruence subgroups with (non-arithmetic) characters, investigations of zeros of Selberg zeta functions for character deformations
Transfer operator method and dynamical zeta functions, transfer operators for character deformations
Approximations of transfer operators, numerical investigations of spectra of transfer operators
Vector-valued period functions, Hecke operators for period functions, relation between period functions and eigenfunctions of transfer operators
Publications
Perturbation of zeros of the Selberg zeta-function for \Gamma_0(4); R. Bruggeman, M. Fraczek, D. Mayer; Experimental Mathematics 22:3 (2013), 217 - 242; arXiv:1201.2324
Note on Section 3: Additional remarks on automorphic forms for \Gamma_0(4) PDF
Symmetries of the transfer operator for \Gamma_0(n) and a character deformation of the Selberg zeta function for \Gamma_0(4); M. Fraczek, D. Mayer; Algebra and Number Theory 6:3 (2012), 587 - 610; arXiv:1011.4441
A realization of the Hecke algebra on the space of period functions for \Gamma_0(n); M. Fraczek, D. Mayer, T. Mühlenbruch; Journal für die reine und angewandte Mathematik 603 (2007), 133 - 163; (Crelle's Journal) arXiv:math/0512355
Theses
Character deformation of the Selberg zeta function for congruence subgroups via the transfer operator; Ph.D. Thesis, Clausthal University of Technology (2012), PDF, see also Character deformations
Spezielle Eigenfunktionen des Transfer-Operators für Hecke Kongruenz Untergruppen; Diploma-Thesis, Clausthal University of Technology (2006), PDF
Aktive Schwingungsdämpfung; Diploma-Thesis, University of Applied Sciences Wedel (2002), (available on request)
Talks
Zeros of the Selberg zeta function and involutions of Maass wave forms; One Day Ergodic Theory Meeting: Noncommutative Geometry, Number Theory and Dynamics, University of Warwick, UK (2014)
Zeros of the Selberg zeta function and involutions of Maass wave forms; Heilbronn Seminar, University of Bristol, UK (2014)
Zeros of the Selberg zeta function and involutions of Maass wave forms; Number Theory Seminar, University of Nottingham, UK (2014)
Zeros of the Selberg zeta function and involutions of Maass wave forms; Number Theory Seminar, University of Warwick, UK (2013)
Spectra of transfer operators and zeta functions; Ergodic Theory and Dynamical Systems Seminar, University of Warwick, UK (2013)
Computation of the Selberg zeta function for the Hecke congruence subgroups with an unitary character; Department of Theoretical Physics, Freiburg University (2011)
Computation of the Selberg zeta function for the Hecke congruence subgroups with an unitary character; Department of Mathematics, Clausthal (2010)
The Phillips and Sarnak Conjecture and Mayer's Transfer Operator; Department of Mathematics, UC Berkeley (2010)
The transfer operator and the zeros of the Selberg zeta function; at Summer School "Large N Limits" in France (2008)
Transfer operator approach to quantum chaos; International Research Training Group "Geometry and Analysis of Symmetries" Research Seminar, Paderborn University (2006); PDF
The Fricke operator on the space of eigenfunctions of the Transfer operator for Hecke congruence subgroups ; Center for Theoretical Physics of the Polish Academy of Sciences, Warsaw (2006); PDF
Spezielle Eigenfunktionen des Transfer-Operators für Hecke Kongruenz Untergruppen; Max Planck Institute for the Physics of Complex Systems, Dresden (2006); PDF
Spezielle Eigenfunktionen des Transfer-Operators für Hecke Kongruenz Untergruppen; Clausthal (2006); PDF