Publications
Preprints
- Period functions for vector-valued Maass cusp forms of real weight, with an application to Jacobi Maass cusp forms (with R. Bruggeman and Y. Choie) (arXiv) 58 pp.
- Equidistribution of cusp points of Hecke triangle groups (with L. Breitkopf and M. Kesseböhmer) (arXiv) 29 pp.
- Symbolic dynamics and transfer operators for Weyl chamber flows: a class of examples (arXiv) 22 pp.
- Zero is a resonance of every Schottky surface (with A. Adam and A. Weiße) (arXiv) 13 pp.
- A geometric reduction theory for indefinite binary quadratic forms over \mathbb{Z}[\lambda] (with V. Spratte) (arXiv) 30 pp.
Articles (peer-reviewed, in publication order)
- Selberg zeta functions, cuspidal accelerations, and existence of strict transfer operator approaches (with P. Wabnitz), to appear in Mem. Am. Math. Soc. (arXiv) 150 pp.
- Counting resonances on hyperbolic surfaces with unitary twists (with M. Doll and K. Fedosova), Commun. Anal. Geom. (2024), Vol. 32, Issue 10, 2805-2887 (journal, arXiv)
- Scattering theory with unitary twists (with M. Doll and K. Fedosova), J. Anal. Math. 153 (2024), 111-167 (journal, arXiv)
- Eigenfunctions of transfer operators and automorphic forms for Hecke triangle groups of infinite covolume (with R. Bruggeman), Mem. Am. Math. Soc. 1423 (2023), vol. 287, 172+vii pp. (journal, arXiv)
- Fourier expansions of vector-valued automorphic functions with non-unitary twists (with K. Fedosova and J. Rowlett), Commun. Number Theory Phys. 17 (2023), no. 1, 173-248 (journal, arXiv)
- Numerical resonances for Schottky surfaces via Lagrange-Chebyshev approximation (with O. Bandtlow, T. Schick, A. Weiße), Stoch. Dyn. 21, No. 03, 2140005, 30 pp. (2021) (journal, arXiv)
- Dynamics of geodesics, and Maass cusp forms (with D. Zagier), Enseign. Math. (2) 66 (2020), 305-340 (journal, arXiv)
- Density of Resonances for covers of Schottky surfaces (with L. Soares), J. Spectr. Theory 10 (2020), no. 3, 1053-1101 (journal, arXiv)
- Eisenstein series twisted with non-expanding cusp monodromies (with K. Fedosova), Ramanujan J. 51 (2020), no. 3, 649-670 (journal, arXiv)
- Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy (with K. Fedosova), Selecta Math. (N.S.) 26 (2020), no. 1, Paper no. 9 (55 p.) (journal, arXiv)
- A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions (with A. Adam), Ergodic Theory Dynam. Systems 40 (2020), no. 3, 612-662 (journal, arXiv)
- Fractal Weyl bounds and Hecke triangle groups (with F. Naud and L. Soares), Electron. Res. Announc. Math. Sci. 26 (2019), 24-35 (journal, arXiv)
- The category of reduced orbifolds in local charts, J. Math. Soc. Japan 69 (2017), no. 2, 755-800 (journal, arXiv)
- Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension (with S. Kadyrov), Ergodic Theory Dynam. Systems 37 (2017), no. 2, 539-563 (journal, arXiv)
- The sup-norm problem for the Siegel modular space of rank two (with V. Blomer), Amer. J. Math. 138 (2016), 999-1027 (journal, arXiv)
- Symbolic dynamics, automorphic functions, and Selberg zeta functions with unitary representations, Contemp. Math. 669 (2016), 205-236 (journal, arXiv)
- Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow Ergodic Theory Dynam. Systems 36 (2016), no. 1, 142-172 (journal, arXiv)
- Escape of mass and entropy for diagonal flows in real rank one situations (with M. Einsiedler and S. Kadyrov), Israel J. Math 245 (2015), Vol. 210, no. 1, 245-295 (journal, arXiv)
- A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area, Comm. Math. Phys. 337 (2015), no. 1, 103-126 (journal, arXiv)
- Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds, Discrete Contin. Dyn. Syst., Ser. A 34 (2014), no. 5, 2173-2241 (journal, arXiv)
- Period functions for Maass cusp forms for \Gamma_0(p): a transfer operator approach, International Mathematics Research Notices (2013) Vol. 14, 3250-3273; (journal, arXiv)
- Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant (with M. Möller), Ergodic Theory Dynam. Systems 33 (2013), no. 1, 247-283 (journal, arXiv)
- A dynamical approach to Maass cusp forms J. Mod. Dyn. 6 (2012), no. 4, 563-596 (journal, arXiv)
- Ford fundamental domains in symmetric spaces of rank one, Geom. Dedicata 147 (2010), 219-276 (journal, arXiv)
- Symbolic dynamics for the geodesic flow on locally symmetric orbifolds of rank one (with J. Hilgert), Infinite Dimensional Harmonic Analysis IV, World Scientific, 2008 (arXiv)
- An upper bound for the period length of a quadratic irrational, Abh. Math. Sem. Univ. Hamburg 77 (2007), 129-136 (journal)
For almost all of my articles one can find preprint versions on the arXiv.
Reports
- Fractal Weyl bounds via transfer operators, Oberwolfach report 22/2023 "Group Actions and Harmonic Analysis in Number Theory" (My report; Full report)
- Resonances of Schottky surfaces, Oberwolfach report 26/2020 "Automorphic Forms and Arithmetic" (My report; Full report)
- Generalized transfer matrices and automorphic functions, Oberwolfach report 55/2017 "Reflection Positivity" (My report; Full report)
- Dynamical characterization of Maass forms, Oberwolfach report 40/2017 "Automorphic Forms and Arithmetic" (My report; Full report)
Qualification Theses
- Dynamical Systems and Automorphic Functions — Laplace eigenfunctions, the geodesic flow, and entropy, Habilitation thesis, University of Göttingen, 48+290 pp. (available on request)
- Symbolic dynamics for the geodesic flow on locally symmetric good orbifolds of rank one, Dissertation thesis, University of Paderborn (printer friendly; for screen) 242 pp.
- Quadratische Formen und reduzierte Matrizen, Diploma thesis, Clausthal University of Technology (available on request)
Editor
- Dynamics: Topology and Numbers. Contemp. Math. 744 (2020) (Editors: P. Moree, A. Pohl, L. Snoha, T. Ward)
- Open Quantum Systems - A Mathematical Perspective. Tutor. Sch. Workshops Math. Sci., Birkhäuser/Springer, Cham, 2019 (Editors: D. Bahns, A. Pohl, I. Witt)