Asymptotics for closed geodesics in a homology class, the finite volume case

DOI10.1215/S0012-7094-87-05536-0zbMath0648.58041OpenAlexW1579439507MaRDI QIDQ1105255

Charles L. Epstein

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-87-05536-0

zbMATH Keywords

perturbation theoryFourier analysisHardy-Littlewood methodclosed geodesics on a hyperbolic manifoldspectral theory of 1-dimensional flat bundles

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Discontinuous groups and automorphic forms (11F99)

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Cites Work

• Unnamed Item
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics
• The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups
• Geodesics in homology classes
• The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
• The spectral theory of geometrically periodic hyperbolic 3-manifolds
• The Polarizability of the Neutron in an Electrostatic Field