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Mathematische Zeitschrift

, Volume 250, Issue 4, pp 939–965 | Cite as

The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations

  • Joshua S. FriedmanEmail author
Article

Abstract

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitary representations. We show that the presence of cuspidal elliptic elements sometimes adds ramification points to the zeta-function. In fact, if Open image in new window is the ring of Eisenstein integers, then the Selberg zeta-function of Open image in new window contains ramification points and is the sixth-root of a meromorphic function.

Keywords

Unitary Representation Trace Formula Selberg Trace Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsStony Brook UniversityStony BrookUSA

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