Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series

DOI10.1016/0022-1236(91)90014-VzbMath0743.58034OpenAlexW1985736575MaRDI QIDQ1174996

Steven Zelditch

Publication date: 25 June 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(91)90014-v

zbMATH Keywords

Eisenstein seriesequidistributioncusp forms

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (13)

Long time quantum evolution of observables on cusp manifolds ⋮ Quantum unique ergodicity for Eisenstein series on \(PSL_ 2(\mathbb{Z}){\setminus}PSL_ 2(\mathbb{R})\) ⋮ Quantum ergodicity for Eisenstein functions ⋮ Equidistribution of cusp forms on \(\text{PSL}_ 2({\mathbb{Z}})\setminus \text{PSL}_ 2({\mathbb{R}})\) ⋮ The quantum unique ergodicity conjecture for thin sets ⋮ Computations of Eisenstein series on Fuchsian groups ⋮ Quantitative quantum ergodicity and the nodal domains of Hecke-Maass cusp forms ⋮ Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions ⋮ Quantum ergodicity for pseudo-Laplacians ⋮ Semiclassical limits for the hyperbolic plane ⋮ On the rate of quantum ergodicity. I: Upper bounds ⋮ On the Topography of Maass Waveforms for PSL(2, Z) ⋮ Around quantum ergodicity

Cites Work

• On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)
• The averaging method and ergodic theory for pseudo-differential operators on compact hyperbolic surfaces
• Ergodicity and eigenfunctions of the Laplacian
• Pseudo-differential analysis on hyperbolic surfaces
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Selberg trace formulae, pseudodifferential operators, and geodesic periods of automorphic forms
• Quasi-modes sur les variétés Riemanniennes
• Prime geodesic theorem.
• Asymptotic behavior of periodic orbits of the horocycle flow and eisenstein series
• Selberg trace formulae and equidistribution theorems for closed geodesics and Laplace eigenfunctions: finite area surfaces
• Fourier coefficients of the resolvent for a Fuchsian group.
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