A RELATIVE TRACE FORMULA FOR A COMPACT RIEMANN SURFACE

DOI10.1142/S1793042111004101zbMath1314.11040arXiv1504.05684OpenAlexW3099559908MaRDI QIDQ5392206

Eric Wambach, Kimball Martin, Mark McKee

Publication date: 8 April 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05684

zbMATH Keywords

compact Riemann surfacerelative trace formulaperiod integralslengths of geodesics

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) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (4)

A symplectic restriction problem ⋮ The hyperbolic lattice point problem in conjugacy classes ⋮ Counting common perpendicular arcs in negative curvature ⋮ Mean value results and \(\Omega\)-results for the hyperbolic lattice point problem in conjugacy classes

Cites Work

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• Local analysis of Selberg's trace formula
• Spectral square means for period integrals of wave functions on real hyperbolic spaces
• A sum formula for a pair of closed geodesics on a hyperbolic surface
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Fourier coefficients of cusp forms
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• Scattering matrices and scattering geodesics of locally symmetric spaces
• The Orthogonal Spectrum of a Hyperbolic Manifold
• Tauberian Theory

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