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

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dc.creatorFriedman, Joshua S.
dc.date2004-10-04
dc.date2004-10-19
dc.date.accessioned2026-07-07T05:12:51Z
dc.date.available2026-07-07T05:12:51Z
dc.descriptionFor 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.
dc.description25 pages, submitted to Mathematische Zeitschrift
dc.identifierhttps://arxiv.org/abs/math/0410067
dc.identifierhttp://arxiv.org/abs/math/0410067
dc.identifierdoi:10.1007/s00209-005-0806-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72736
dc.subjectNumber Theory
dc.subjectSpectral Theory
dc.subject11F72; 11M36
dc.titleThe Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations
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