Quantum unique ergodicity for Eisenstein series on \(PSL_ 2(\mathbb{Z}){\setminus}PSL_ 2(\mathbb{R})\)

DOI10.5802/aif.1442zbMath0820.11040OpenAlexW2073627973MaRDI QIDQ1891342

Dmitry Jakobson

Publication date: 30 May 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1994__44_5_1477_0

zbMATH Keywords

congruence subgroupsWigner distributionsmicrolocal equidistribution theorem

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (20)

A central limit theorem for integrals of random waves ⋮ Long time quantum evolution of observables on cusp manifolds ⋮ Equidistribution of Eisenstein series on geodesic segments ⋮ Recent progress on the quantum unique ergodicity conjecture ⋮ Equidistribution of cusp forms on \(\text{PSL}_ 2({\mathbb{Z}})\setminus \text{PSL}_ 2({\mathbb{R}})\) ⋮ Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms ⋮ Nodal domains of Maass forms. I ⋮ The quantum unique ergodicity conjecture for thin sets ⋮ Quantum unique ergodicity of degenerate Eisenstein series on \(\mathrm{GL}(n)\) ⋮ Intersecting geodesics on the modular surface ⋮ Microlocal limits of Eisenstein functions away from the unitarity axis ⋮ Quantum limits of Eisenstein series in ℍ³ ⋮ Triple product \(L\)-functions and quantum chaos on \(\mathrm{SL}(2,\mathbb C)\) ⋮ Spectra of hyperbolic surfaces ⋮ Quantum unique ergodicity for half-integral weight automorphic forms ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers ⋮ Hecke theory and equidistribution for the quantization of linear maps of the torus ⋮ Eisenstein quasimodes and semiclassical behavior of expectation values ⋮ Around quantum ergodicity ⋮ Eisenstein quasimodes and QUE

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• Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series
• Density of integer points on affine homogeneous varieties
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
• The square mean of Dirichlet series associated with cusp forms
• 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
• Harmonic Analysis in Phase Space. (AM-122)
• Fourier coefficients of the resolvent for a Fuchsian group.

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