The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps

DOI10.1007/s00208-009-0408-7zbMath1236.11081OpenAlexW1997348260MaRDI QIDQ845756

Yasuro Gon, Jinsung Park

Publication date: 29 January 2010

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-009-0408-7

zbMATH Keywords

functional equationsSelberg trace formulameromorphic extensionsSelberg zeta-functionrepresentations for real hyperbolic manifolds with cuspsRuelle zeta-functionsingularity of Ruelle zeta-function at originweighted unipotent orbital integrals

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps ⋮ Gallagherian PGT on some compact Riemannian manifolds of negative curvature ⋮ The twisted Selberg trace formula and the twisted Selberg zeta function for compact orbifolds ⋮ Selberg type zeta function for the Hilbert modular group of a real quadratic field ⋮ Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces ⋮ Analytic torsions for hyperbolic manifolds with cusps ⋮ Ruelle zeta function for odd dimensional hyperbolic manifolds with cusps ⋮ Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps ⋮ Reidemeister torsion, complex volume and the Zograf infinite product for hyperbolic 3-manifolds ⋮ Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy ⋮ Ruelle zeta function for cofinite hyperbolic Riemann surfaces with ramification points ⋮ Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps

Cites Work

• Unnamed Item
• Unnamed Item
• \(L^ 2\)-index and the Selberg trace formula
• Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps
• The trace class conjecture in the theory of automorphic forms
• Analytic torsions for hyperbolic manifolds with cusps
• Zeta functions of Selberg's type associated with homogeneous vector bundles
• Analytic torsion and closed geodesics on hyperbolic manifolds
• On the Plancherel measure for linear Lie groups of rank one
• On a theorem of Osborne and Warner. Multiplicities in the cuspidal spectrum
• Poincaré series for \(SO(n,1)\)
• The Fourier transform on semisimple Lie groups of real rank one
• Zeta-functions for expanding maps and Anosov flows
• Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one
• Multiplicities of the integrable discrete series: the case of a nonuniform lattice in an R-rank one semisimple group
• Gamma factors of Selberg zeta functions and functional equation of Ruelle zeta functions
• Cohomological theory of dynamical zeta functions
• The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein
• On the analytic continuation of rank one Eisenstein series
• The expressions of the Harish-Chandra \(C\)-functions of semisimple Lie groups \(\text{Spin}(n,1)\), \(\text{SU}(n,1)\)
• The wave trace for Riemann surfaces
• Equidistribution of holonomy about closed geodesics
• Gamma factors and Plancherel measures
• Ruelle zeta function for odd dimensional hyperbolic manifolds with cusps
• The zeta functions of Ruelle and Selberg. I
• On the Selberg trace formula in the case of compact quotient
• Analyse harmonique des formes différentielles sur l'espace hyperbolique réel II. Transformation de Fourier sphérique et applications
• Secondary invariants and the singularity of the Ruelle zeta-function in the central critical point
• The Fourier transforms of weighted orbital integrals on simisimple groups of real rank one.
• Multiple sine functions
• The Weil-étale topology on schemes over finite fields
• An invariant trace formula for rank one lattices
• Théorie spectrale de quelques variétés à bouts
• Symbolic Dynamics for Hyperbolic Flows
• An analog of the Iwasawa conjecture for a compact hyperbolic threefold
• Eta invariants and regularized determinants for odd dimensional hyperbolic manifolds with cusps
• Spectral zeta functions for compact symmetric spaces of rank one
• The Gauss-Bonnet formula for hyperbolic manifolds of finite volume