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arXiv · 0912.2236

The transfer operator for the Hecke triangle groups

Dieter Mayer·Tobias Mühlenbruch·Fredrik Strömberg
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Abstract

In this paper we extend the transfer operator approach to Selberg's zeta function for cofinite Fuchsian groups to the Hecke triangle groups G_q, q=3,4,..., which are non-arithmetic for q \not= 3,4,6. For this we make use of a Poincare map for the geodesic flow on the corresponding Hecke surfaces which has been constructed in arXiv:0801.3951 and which is closely related to the natural extension of the generating map for the so called Hurwitz-Nakada continued fractions. We derive simple functional equations for the eigenfunctions of the transfer operator which for eigenvalues rho =1 are expected to be closely related to the period functions of Lewis and Zagier for these Hecke triangle groups.

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Dieter Mayer, Tobias Mühlenbruch, Fredrik Strömberg. 2010-03-15. The transfer operator for the Hecke triangle groups. https://doi.org/10.3934/dcds.2012.32.2453

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