Artin formalism for Selberg zeta functions of co-finite Kleinian groups
| dc.creator | Brenner, Eliot | |
| dc.creator | Spinu, Florin | |
| dc.date | 2008-01-13 | |
| dc.date | 2008-01-19 | |
| dc.date.accessioned | 2026-07-07T08:55:07Z | |
| dc.date.available | 2026-07-07T08:55:07Z | |
| dc.description | Let $Γ\backslash\mathbb H^3$ be a finite-volume quotient of the upper-half space, where $Γ\subset {\rm SL}(2,\mathbb C)$ is a discrete subgroup. To a finite dimensional unitary representation $χ$ of $Γ$ one associates the Selberg zeta function $Z(s;Γ;χ)$. In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if $\tildeΓ$ is a finite index group extension of $Γ$ in ${\rm SL}(2,\mathbb C)$, and $π={\rm Ind}_Γ^{\tildeΓ}χ$ is the induced representation, then $Z(s;Γ;χ)=Z(s;\tildeΓ;π)$. In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely $ϕ(s;Γ;χ)=ϕ(s;\tildeΓ;π)$, for an appropriate normalization of the Eisenstein series. | |
| dc.description | 14 pages. In v2 added key reference and clarified relationship to certain results in the literature | |
| dc.identifier | https://arxiv.org/abs/0801.1938 | |
| dc.identifier | http://arxiv.org/abs/0801.1938 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146174 | |
| dc.subject | Number Theory | |
| dc.subject | 11F72; 11M36 | |
| dc.title | Artin formalism for Selberg zeta functions of co-finite Kleinian groups | |
| dc.type | text |