Trace formula for compact \(\Gamma \setminus PSL_ 2({\mathbb{R}})\) and the equidistribution theory of closed geodesics

DOI10.1215/S0012-7094-89-05902-4zbMath0686.10024MaRDI QIDQ1262336

Steven Zelditch

Publication date: 1989

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

zbMATH Keywords

closed geodesicdiscrete, cocompact subgrouptrace formulas for pseudodifferential operators

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Discrete subgroups of Lie groups (22E40) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

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Zeta functions and periodic orbit theory: A review ⋮ Equidistribution of minimal hypersurfaces for generic metrics ⋮ LOCAL AVERAGE OF THE HYPERBOLIC CIRCLE PROBLEM FOR FUCHSIAN GROUPS ⋮ A prime geodesic theorem for \(\mathrm{SL}_4\) ⋮ Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux ⋮ A prime geodesic theorem for higher rank. II: Singular geodesics ⋮ Semiclassical limits for the hyperbolic plane ⋮ Geodesics in homology classes and periods of automorphic forms

Cites Work

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• On the zeros of Maass wave form 𝐿-functions
• The Riemann Hypothesis for Selberg's Zeta-Function and the Asymptotic Behavior of Eigenvalues of the Laplace Operator
• The Equidistribution of Closed Geodesics