Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group

DOI10.2307/120977zbMath0969.11019arXivdg-ga/9603003OpenAlexW2040404114MaRDI QIDQ1293372

Martin Olbrich, Ulrich Bunke

Publication date: 14 May 2001

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9603003

zbMATH Keywords

divisorgroup cohomologySelberg zeta-functioninvariant distributionhigher Euler characteristicPatterson conjectureconvex cocompact hyperbolic group

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Cohomology of arithmetic groups (11F75)

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Semiclassical formulae for Wigner distributions ⋮ Spectral gaps, additive energy, and a fractal uncertainty principle ⋮ Hyperfunctions in hyperbolic geometry ⋮ Fractal Weyl laws for asymptotically hyperbolic manifolds ⋮ Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume ⋮ Higher rank quantum-classical correspondence ⋮ Classical and quantum resonances for hyperbolic surfaces ⋮ The Selberg zeta function for convex co-compact Schottky groups ⋮ Eta invariant and Selberg zeta function of odd type over convex co-compact hyperbolic manifolds ⋮ Resolvent of the Laplacian on geometrically finite hyperbolic manifolds ⋮ The spectrum of Kleinian manifolds ⋮ Wave decay on convex co-compact hyperbolic manifolds ⋮ A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions ⋮ Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds ⋮ The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein ⋮ Resonance chains and geometric limits on Schottky surfaces ⋮ Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

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