$\mathrm{\Gamma }$-Cohomology and the Selberg Zeta Function

We propose a new method for studying $n$- and $\mathrm{\Gamma }$-cohomology of globalizations of Harish-Chandra modules, where $G=KAN$ is a rank one semisimple Lie group, $\mathrm{\Gamma }$ is a discrete subgroup of $G$ and $n=Lie(N)$. We prove a conjecture of Patterson relating the singularities of Selberg zeta functions with the $\mathrm{\Gamma }$-cohomology of principal series representations if $\mathrm{\Gamma }$ is cocompact and torsion free.