The Selberg trace formula and the Ruelle zeta function for compact hyperbolics

DOI10.1007/BF02942321zbMath0716.53044MaRDI QIDQ753158

Anton Deitmar

Publication date: 1989

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

zbMATH Keywords

differential formshyperbolic manifoldtrace formulaRuelle zeta functionSelberg type

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Zeta functions and periodic orbit theory: A review, Anomalies and analytic torsion on hyperbolic manifolds, A refinement of strong multiplicity one for spectra of hyperbolic manifolds, On Partition Functions of Hyperbolic Three-Geometry and Associated Hilbert Schemes, Ray-Singer torsion for a hyperbolic 3-manifold and asymptotics of Chern-Simons-Witten invariant, Kissing numbers of closed hyperbolic manifolds, Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies, Semiclassical approximation for Chern-Simons theory and \(3\)-hyperbolic invariants., Complex Topological Invariants of Three-Hyperbolic Manifolds

Cites Work

• Analytic torsion and closed geodesics on hyperbolic manifolds
• The Minakshisundaram-Pleijel Coefficients for the Vector Valued Heat Kernel on Compact Locally Symmetric Spaces of Negative Curvature
• On the Selberg trace formula in the case of compact quotient
• The Plancherel formula for the Lorentz group of $n$-th order
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