Poincaré series and zeta functions for surface group actions on \(\mathbb{R}\)-trees (Q1380094)

Let \(\Gamma\) be a discrete group acting on \(H^n\). Under certain circumstances one can show that appropriate generating series for counting lattice points and conjugacy classes have good analytic properties. The combinatorial analogues, in the context of hyperbolic groups, are also known (they are due to Cannon and Gromov). The purpose of this paper is to establish analogous properties in some rather special cases associated with surface groups acting on \(\mathbb{R}\)-trees. The arguments used are variants of those used in the case of simplicial trees.