Paul Wabnitz - Transfer operator approach to Selberg's zeta function

We consider properly discontinuous group actions on the real hyperbolic 2-space. Building on previous work by A. Pohl and various coauthors, we give an overview on how to construct certain transfer operators for the geodesic flow suitable for a thermodynamic formalism approach to the Selberg zeta function Z. This is a crucial step in the rigorously constructive proof of the correlation between the zeros of Z and a certain class of L2-eigenfunctions of the Laplace–-Beltrami operator on the orbit space.