Equidistribution of Eisenstein Series for Convex Co-compact Hyperbolic Manifolds

DOI10.1007/978-3-0348-0466-0_21zbMath1271.58016arXiv1107.2655OpenAlexW2027331411MaRDI QIDQ4912961

Frédéric Naud, Colin Guillarmou

Publication date: 2 April 2013

Published in: American Journal of Mathematics, Microlocal Methods in Mathematical Physics and Global Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.2655

zbMATH Keywords

Eisenstein seriesHausdorff dimensionquantum ergodicityhyperbolic manifoldsharmonic densityergodic geodesic flowco-finite Fuchsian groupGutzwiller type formulamicro local extension

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (6)

Long time quantum evolution of observables on cusp manifolds ⋮ Microlocal limits of Eisenstein functions away from the unitarity axis ⋮ Distorted plane waves on manifolds of nonpositive curvature ⋮ On the nodal lines of Eisenstein series on Schottky surfaces ⋮ Distorted plane waves in chaotic scattering ⋮ Around quantum ergodicity

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