$Γ$-Cohomology and the Selberg Zeta Function

Details $Γ$-Cohomology and the Selberg Zeta Function $Γ$-Cohomology and the Selberg Zeta Function

1994-11-18

arxiv.org/abs/dg-ga/9411004v1

Mathematics

Differential Geometry

21 pages, LATEX

Scientific paper

We propose a new method for studying $n$- and $\Gamma$-cohomology of globalizations of Harish-Chandra modules, where $G=KAN$ is a rank one semisimple Lie group, $\Gamma$ 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 $\Gamma$-cohomology of principal series representations if $\Gamma$ is cocompact and torsion free.

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