Publications

Preprints

  1. 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.
  2. Equidistribution of cusp points of Hecke triangle groups (with L. Breitkopf and M. Kesseböhmer) (arXiv) 29 pp.
  3. Symbolic dynamics and transfer operators for Weyl chamber flows: a class of examples (arXiv) 22 pp.
  4. Zero is a resonance of every Schottky surface (with A. Adam and A. Weiße) (arXiv) 13 pp.
  5. 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)

  1. 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.
  2. 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)
  3. Scattering theory with unitary twists (with M. Doll and K. Fedosova), J. Anal. Math. 153 (2024), 111-167 (journal, arXiv)
  4. 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)
  5. 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)
  6. 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)
  7. Dynamics of geodesics, and Maass cusp forms (with D. Zagier), Enseign. Math. (2) 66 (2020), 305-340 (journal, arXiv)
  8. Density of Resonances for covers of Schottky surfaces (with L. Soares), J. Spectr. Theory 10 (2020), no. 3, 1053-1101 (journal, arXiv)
  9. Eisenstein series twisted with non-expanding cusp monodromies (with K. Fedosova), Ramanujan J. 51 (2020), no. 3, 649-670 (journal, arXiv)
  10. 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)
  11. 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)
  12. Fractal Weyl bounds and Hecke triangle groups (with F. Naud and L. Soares), Electron. Res. Announc. Math. Sci. 26 (2019), 24-35 (journal, arXiv)
  13. The category of reduced orbifolds in local charts, J. Math. Soc. Japan 69 (2017), no. 2, 755-800 (journal, arXiv)
  14. 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)
  15. The sup-norm problem for the Siegel modular space of rank two (with V. Blomer), Amer. J. Math. 138 (2016), 999-1027 (journal, arXiv)
  16. Symbolic dynamics, automorphic functions, and Selberg zeta functions with unitary representations, Contemp. Math. 669 (2016), 205-236 (journal, arXiv)
  17. 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)
  18. 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)
  19. 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)
  20. 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)
  21. 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)
  22. 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)
  23. A dynamical approach to Maass cusp forms J. Mod. Dyn. 6 (2012), no. 4, 563-596 (journal, arXiv)
  24. Ford fundamental domains in symmetric spaces of rank one, Geom. Dedicata 147 (2010), 219-276 (journal, arXiv)
  25. 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)
  26. 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