2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152023We propose a new method for studying $n$- and $Γ$-cohomology of globalizations of Harish-Chandra modules, where $G=KAN$ is a rank one semisimple Lie group, $Γ$ 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 $Γ$-cohomology of principal series representations if $Γ$ is cocompact and torsion free.21 pages, LATEXDifferential Geometrytext