Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy

Abstract

We initiate the study of Selberg zeta functions Z_{Gamma ,chi } for geometrically finite Fuchsian groups Gamma and finite-dimensional representations chi with non-expanding cusp monodromy. We show that for all choices of (Gamma ,chi ), the Selberg zeta function Z_{Gamma ,chi } converges on some half-plane in mathbb {C}. In addition, under the assumption that Gamma admits a strict transfer operator approach, we show that Z_{Gamma ,chi } extends meromorphically to all of mathbb {C}.