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Discontinuous groups on three-dimensional hyperbolic space: analytical theory and arithmetic applications. (English. Russian original) Zbl 0527.10018

Russ. Math. Surv. 38, No. 1, 137-168 (1983); translation from Usp. Mat. Nauk 38, No. 1(229), 119-147 (1983). Correction in Usp. Mat. Nauk 38, No. 6(234), 177-178 (Russian) (1983).

MSC:

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