Period functions for Maass cusp forms for Γ0(p)\Gamma_0(p): a transfer operator approach

We characterize the Maass cusp forms for Hecke congruence subgroups of prime level as 1-eigenfunctions of a finite-term transfer operator.Comment: 17 pages, 6 figure

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

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 $\mathbb{C}$.Comment: 46 pages, v4: added results on nonconvergence beyond NECM; added proofs for meromorphic continuation of derivatives of the Lerch transcendent; final version accepted for publicatio