On the distribution of the lengths of closed geodesics of a compact surface with totally geodesic boundary.

DOI10.1215/S0012-7094-86-05345-7zbMath0611.53042OpenAlexW1502090468MaRDI QIDQ1087154

Laurent Guillopé

Publication date: 1986

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-86-05345-7

zbMATH Keywords

Selberg trace formulahyperbolic planeSelberg zeta functionclosed geodesicsasymptotics for the distribution functionscompact Riemann surfaces with boundary

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Irrationality; linear independence over a field (11J72)

Related Items (14)

Selberg trace formula for bordered Riemann surfaces: Hyperbolic, elliptic and parabolic conjugacy classes, and determinants of Maass-Laplacians ⋮ Lower bound on the number of non-simple closed geodesics on surfaces ⋮ Closed geodesics with prescribed intersection numbers ⋮ Resonances and weighted zeta functions for obstacle scattering via smooth models ⋮ Prime orbit theorems for expanding Thurston maps: Dirichlet series and orbifolds ⋮ Self-intersection on Pair of Pants ⋮ The Selberg zeta function for convex co-compact Schottky groups ⋮ Resolvent of the Laplacian on geometrically finite hyperbolic manifolds ⋮ Expanding maps on Cantor sets and analytic continuation of zeta functions ⋮ On the spectral theory and dynamics of asymptotically hyperbolic manifolds ⋮ Kleinian Groups, Laplacian on Forms and Currents at Infinity ⋮ Geometric control in the presence of a black box ⋮ Geometry of Riemann surfaces based on closed geodesics ⋮ The Selberg trace formula for bordered Riemann surfaces

Cites Work

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• Boundary problems for pseudo-differential operators
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• On Poincaré's theorem for fundamental polygons
• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• Correction to: Silberg' trace formua as applied to a compact riemann surface by H. P. Mckean, comm. pure appl. math. 25, pp. 225‐246,1972

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