Computation of Selberg zeta functions on Hecke triangle groups

In this paper, a heuristic method to compute the Selberg zeta function for Hecke triangle groups, $G_q$ ($q>=3$) is described. The algorithm is based on the transfer operator method and an overview of the relevant background is given. We give numerical support for the claim that the method works and can be used to compute the Selberg Zeta function for $G_q$ to any desired precision. We also present some numerical results obtained by implementing the algorithm.