Discontinuous groups on three-dimensional hyperbolic space: analytical theory and arithmetic applications

DOI10.1070/RM1983v038n01ABEH003384zbMath0527.10018MaRDI QIDQ3043232

Jens Mennicke, Jürgen Elstrodt, Fritz J. Grunewald

Publication date: 1983

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

zbMATH Keywords

hyperbolic LaplacianSelberg trace formulaspectral theorySelberg zeta-functionprime geodesic theoremdiscrete subgroups of PSL(2,C)cocompact groupsconjugacy classes in orthogonal groupshyperbolic lattice-point problemprogress reportSiegel theory of quadratic formsstructure of unit groups

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Modular and automorphic functions (11F03) Discrete subgroups of Lie groups (22E40) Ergodic theorems, spectral theory, Markov operators (37A30) Geodesics in global differential geometry (53C22) Lattice points in specified regions (11P21) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Hurwitz and Lerch zeta functions (11M35) Classical groups (11E57) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

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