Geodesics in homology classes and periods of automorphic forms

DOI10.1016/0001-8708(91)90004-QzbMath0732.11023OpenAlexW2068862206MaRDI QIDQ809122

Steven Zelditch

Publication date: 1991

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(91)90004-q

zbMATH Keywords

Poincaré seriesasymptotic behaviourcompact Riemann surfacetrace formulauniform distributionclosed geodesicsautomorphic formhomology classEichler cohomology

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Geodesics in global differential geometry (53C22) 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 (3)

Dynamical 𝐿-functions and homology of closed orbits ⋮ Closed geodesics and periods of automorphic forms ⋮ THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW

Cites Work

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• Geodesics in homology classes
• Selberg trace formulae, pseudodifferential operators, and geodesic periods of automorphic forms
• Asymptotics for closed geodesics in a homology class, the finite volume case
• Trace formula for compact \(\Gamma \setminus PSL_ 2({\mathbb{R}})\) and the equidistribution theory of closed geodesics
• Homology of closed geodesics in a negatively curved manifold
• Eichler-Shimura Homology, Intersection Numbers and Rational Structures on Spaces of Modular Forms
• The weyl calculus of pseudo-differential operators

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