A sum formula for a pair of closed geodesics on a hyperbolic surface

DOI10.1215/00127094-2008-024zbMath1195.11073OpenAlexW2002239621MaRDI QIDQ935193

Nigel J. E. Pitt

Publication date: 5 August 2008

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

Full work available at URL: https://doi.org/10.1215/00127094-2008-024

zbMATH Keywords

geodesicFuchsian groupLaplacianMehler-Fock transformsummation formulaperiod integral

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (4)

A symplectic restriction problem ⋮ Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature ⋮ A RELATIVE TRACE FORMULA FOR A COMPACT RIEMANN SURFACE ⋮ Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces

Cites Work

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• Local analysis of Selberg's trace formula
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Closed geodesics, periods and arithmetic of modular forms
• Selberg trace formulae, pseudodifferential operators, and geodesic periods of automorphic forms
• On pairs of closed geodesics on hyperbolic surfaces
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• Prime geodesic theorem.
• Fourier coefficients of the resolvent for a Fuchsian group.

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