Eisenstein matrix and existence of cusp forms in rank one symmetric spaces

DOI10.1007/BF01895514zbMath0785.11034MaRDI QIDQ2366710

Andre Reznikov

Publication date: 31 August 1993

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58113

zbMATH Keywords

spectrumEisenstein seriessymmetric spacescattering matrixarithmetic latticenon-congruence lattices

Mathematics Subject Classification ID

Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

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The scattering matrix for the Hilbert modular group ⋮ Asymptotics of Automorphic Spectra and the Trace Formula ⋮ Fourier expansion of light‐cone Eisenstein series ⋮ Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds ⋮ On the remainder term in the Weyl law for cofinite Kleinian groups with finite dimensional unitary representation ⋮ Explicit formulas for the spectral side of the trace formula of ${\rm SL(2)}$ ⋮ Elliptic factors of Selberg zeta functions ⋮ Spectral asymptotics for arithmetic quotients of \(\text{SL}(n,{\mathbb R})/\text{SO}(n)\) ⋮ Generators of a Picard modular group in two complex dimensions ⋮ On the remainder term of the Weyl law for congruence subgroups of Chevalley groups ⋮ Prime geodesic theorem for higher-dimensional hyperbolic manifold ⋮ Spectral means of central values of automorphic 𝐿-functions for 𝐺𝐿(2) ⋮ On the asymptotic formula of Kuznetsov and existence of generic cusp forms

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