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DCDS

In this paper we extend the transfer operator approach to Selberg's zeta function for cofinite
Fuchsian groups to the Hecke triangle groups $G_q,\, q=3,4,\ldots$, which are non-arithmetic for
$q\not= 3,4,6$. For this we make use of a Poincar\'e map for the geodesic flow on the corresponding
Hecke surfaces, which has been constructed in [13], and which is closely related to the natural extension of the generating map for the
so-called Hurwitz-Nakada continued fractions.
We also derive 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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