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

Other

• Numerische Berechnungen der Periodenfunktionen, der Hecke-Operatoren und der Fricke-Operatoren für Gamma_0(n); Clausthal (2006); PDF

• Transfer Operatoren; Clausthal (2005); PDF