Selberg trace formulae, pseudodifferential operators, and geodesic periods of automorphic forms

DOI10.1215/S0012-7094-88-05613-XzbMath0646.10024MaRDI QIDQ1103665

Steven Zelditch

Publication date: 1988

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

zbMATH Keywords

eigenvalueseigenfunctionsequidistributionSelberg trace formulageodesic flowLaplacianpseudodifferential operatorautomorphic formlength spectrumlengths of closed geodesics

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items (9)

Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature ⋮ Zeta functions and periodic orbit theory: A review ⋮ Uniform distribution of eigenfunctions on compact hyperbolic surfaces ⋮ LOCAL AVERAGE OF THE HYPERBOLIC CIRCLE PROBLEM FOR FUCHSIAN GROUPS ⋮ Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series ⋮ A sum formula for a pair of closed geodesics on a hyperbolic surface ⋮ Trace formula for compact \(\Gamma \setminus PSL_ 2({\mathbb{R}})\) and the equidistribution theory of closed geodesics ⋮ On pairs of closed geodesics on hyperbolic surfaces ⋮ Geodesics in homology classes and periods of automorphic forms

Cites Work

• Pseudo-differential analysis on hyperbolic surfaces
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Topics in harmonic analysis on homogeneous spaces
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• On the existence of cusp forms over function fields.
• The Equidistribution of Closed Geodesics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Selberg trace formulae, pseudodifferential operators, and geodesic periods of automorphic forms