On the cuspidal spectrum for finite volume symmetric spaces

DOI10.4310/JDG/1214436921zbMath0494.58029OpenAlexW1533607772WikidataQ115188058 ScholiaQ115188058MaRDI QIDQ1169195

Harold Donnelly

Publication date: 1982

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214436921

zbMATH Keywords

asymptotic upper bound for the number of linearly independent cuspidal eigenfunctionsLaplacian acting on cuspidal functionsnoncompact locally symmetric space of finite volume

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential geometry of symmetric spaces (53C35) Differential complexes (58J10) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (19)

Eisenstein matrix and existence of cusp forms in rank one symmetric spaces ⋮ A trace formula for coverings of connected reductive groups. III: Development of spectral closure ⋮ Relative trace formulas for unitary hyperbolic spaces ⋮ Isolation of the cuspidal spectrum: the function field case ⋮ On the analytic continuation of rank one Eisenstein series ⋮ Finite energy and totally geodesic maps from locally symmetric spaces of finite volume ⋮ Analytic properties of spherical cusp forms on \(\mathrm{GL}(n)\) ⋮ Asymptotics of Automorphic Spectra and the Trace Formula ⋮ Optimal Diophantine exponents for \(\mathrm{SL}(n)\) ⋮ \(L^ 2\)-index theorems on locally symmetric spaces ⋮ Weyl's law for the cuspidal spectrum of \(\mathrm{SL}_n\). ⋮ Equidistribution of holonomy about closed geodesics ⋮ Sato-Tate equidistribution for families of Hecke-Maass forms on \(\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)\) ⋮ Density results for automorphic forms on Hilbert modular groups II ⋮ A spectral mean value theorem for \(\text{GL}(3)\) ⋮ On the remainder term of the Weyl law for congruence subgroups of Chevalley groups ⋮ Global automorphic Sobolev theory and the automorphic heat kernel ⋮ Exceptional sequences of eigenfunctions for hyperbolic manifolds ⋮ Bias of root numbers for Hilbert newforms of cubic level

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