1. The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations
- Author
-
Joshua Samuel Friedman
- Subjects
Ring (mathematics) ,Pure mathematics ,11F72 ,11M36 ,Mathematics - Number Theory ,Mathematics::Number Theory ,General Mathematics ,Divisor (algebraic geometry) ,Mathematics::Spectral Theory ,Unitary state ,Riemann zeta function ,Mathematics - Spectral Theory ,symbols.namesake ,Selberg trace formula ,Eisenstein integer ,FOS: Mathematics ,symbols ,Number Theory (math.NT) ,Selberg zeta function ,Spectral Theory (math.SP) ,Mathematics ,Meromorphic function - 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 point to the zeta function. In fact, if D is the ring of Eisenstein integers, then the Selberg zeta-function of PSL(2,D) contains ramification points and is the sixth-root of a meromorphic function., 25 pages, submitted to Mathematische Zeitschrift
- Published
- 2005
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