$\Gamma$-Cohomology and the Selberg Zeta Function

Ulrich Bunke; Martin Olbrich

$\Gamma$-Cohomology and the Selberg Zeta Function

dg-ga 2008-02-03 v1 Differential Geometry

Authors: Ulrich Bunke , Martin Olbrich

Abstract

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.

Keywords

Gamma-cohomology Selberg zeta function Harish-Chandra modules semisimple Lie group discrete subgroup principal series representations

Cite

@article{arxiv.dg-ga/9411004,
  title  = {$\Gamma$-Cohomology and the Selberg Zeta Function},
  author = {Ulrich Bunke and Martin Olbrich},
  journal= {arXiv preprint arXiv:dg-ga/9411004},
  year   = {2008}
}

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21 pages, LATEX

$\Gamma$-Cohomology and the Selberg Zeta Function

Abstract

Keywords

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