Quantum variance for Hecke eigenforms☆

DOI10.1016/j.ansens.2004.08.001zbMath1121.11042OpenAlexW2044477056MaRDI QIDQ4651831

Wenzhi Luo, Peter C. Sarnak

Publication date: 22 February 2005

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2004_4_37_5_769_0

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items (19)

Quantum variance for dihedral Maass forms ⋮ Quantitative non-vanishing of central values of certain \(L\)-functions on \(\mathrm{GL}(2) \times \mathrm{GL}(3)\) ⋮ Bounds on shifted convolution sums for Hecke eigenforms ⋮ The variance of closed geodesics in balls and annuli on the modular surface ⋮ Quantum variance and ergodicity for the baker's map ⋮ The quantum unique ergodicity conjecture for thin sets ⋮ Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves ⋮ Wide moments of L-functions. I: Twists by class group characters of imaginary quadratic fields ⋮ Small‐scale equidistribution of Hecke eigenforms at infinity ⋮ Improved subconvexity bounds for 𝐺𝐿(2)×𝐺𝐿(3) and 𝐺𝐿(3) 𝐿-functions by weighted stationary phase ⋮ Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces ⋮ Shifted convolution of cusp-forms with \(\theta \)-series ⋮ Bounds for twisted symmetric square L-functions via half-integral weight periods ⋮ Small scale equidistribution of eigenfunctions on the torus ⋮ Computations of Eisenstein series on Fuchsian groups ⋮ Quantum variance of Maass-Hecke cusp forms ⋮ Quantitative quantum ergodicity and the nodal domains of Hecke-Maass cusp forms ⋮ The spectral decomposition of \(|\theta |^2\) ⋮ Automorphic forms and arithmetic. Abstracts from the workshop held August 30 -- September 5, 2020 (hybrid meeting)

Cites Work

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