The divisor of Selberg's zeta function for Kleinian groups

Citation
Sj. Patterson et Pa. Perry, The divisor of Selberg's zeta function for Kleinian groups, DUKE MATH J, 106(2), 2001, pp. 321-390
Citations number
77
Categorie Soggetti
Mathematics
Journal title
DUKE MATHEMATICAL JOURNAL
ISSN journal
00127094 → ACNP
Volume
106
Issue
2
Year of publication
2001
Pages
321 - 390
Database
ISI
SICI code
0012-7094(20010201)106:2<321:TDOSZF>2.0.ZU;2-8
Abstract
We compute the divisor of Selberg's zeta function for convex cocompact, tor sion-free discrete groups Gamma acting on a real hyperbolic space of dimens ion n + 1. The divisor is determined by the eigenvalues and scattering pole s of the Laplacian on X = Gamma \Hn+1 together with the Euler characteristi c of X compactified to a manifold with boundary. Ifn is even, the singulari ties of the zeta function associated to the Euler characteristic of X are i dentified using work of U. Bunke and M. Olbrich.