Some remarks on discrete subgroups of \(SL_ 2({\mathbb{C}})\). (English. Russian original) Zbl 0672.10019
J. Sov. Math. 46, No. 2, 1760-1788 (1989); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 162, 77-106 (1987).
See the review in Zbl 0629.10020.
MSC:
11F27 | Theta series; Weil representation; theta correspondences |
20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
22E40 | Discrete subgroups of Lie groups |
11F06 | Structure of modular groups and generalizations; arithmetic groups |
58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
11E45 | Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) |
20H25 | Other matrix groups over rings |
Keywords:
first eigenvalue; Laplacian; discrete spectrum; fundamental; domains; discrete subgroups of \(SL_ 2({\mathbb{C}})\); rattlesnake; volume; Roelcke’s method; cocompact discrete groups; binary Hermitian; forms; Dirichlet series; integral equivalence; genus; explicit; formulas; number of representation of integers; Braun-Siegel; theorem; quaternary quadratic formsCitations:
Zbl 0629.10020References:
[1] | A. Borel, ?Commensurability classes and volumes of hyperbolic 3-manifolds,? Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV, Ser. 8, 1?33 (1981). · Zbl 0473.57003 |
[2] | H. Braun, Zur theorie der hermitischen Formen,? Abh. Math. Sem. Univ. Hamburg,14, 61?150 (1941). · Zbl 0025.01603 · doi:10.1007/BF02940742 |
[3] | J. Elstrodt, F. Grunewald, and J. Mennicke, ?Zeta-functions of binary Hermitian forms and special values of Eisenstein series on three-dimensional hyperbolic space, Math. Ann.,277, 655?708 (1987). · Zbl 0659.10021 · doi:10.1007/BF01457865 |
[4] | F. Grunewald and J. Schwermer, ?Free non-abelian quotients of SL2 over orders of imaginary quadratic number fields,? J. Algebra,69, 298?304 (1981). · Zbl 0461.20026 · doi:10.1016/0021-8693(81)90206-4 |
[5] | G. Ligozat,?Courbes modulaires de genre 1,? Bull. Soc. Math. Fr. Mem., 43 (1975). · Zbl 0322.14011 |
[6] | G. A. Margulis, ?Factor groups of discrete subgroups and measure theory,? Funkts. Anal. Prilozh.,12, 64?67 (1978). |
[7] | G. Otremba, ?Zur Theorie der hermiteschen Formen in imaginär-quadratischen Zahlkörpern,? J. Reine Angew. Math.,249, 1?19 (1971). · Zbl 0221.12007 |
[8] | H. Petersson, ?Modulfunktionen und quadratische Formen,? Springer-Verlag, Berlin-Heidel-berg-New York (1982). · Zbl 0493.10033 |
[9] | W. Roelcke, ?Uber die Wellengleichung bei Grenzkreisgruppen erster Art,? Sitzungsber. Heidelberger Akad. Wiss., Math.-Naturwiss. Kl., 1953/55,4, Abhandlung (1956). |
[10] | J. Rohlfs, ?On the cuspidal cohomology of the Bianchi modular groups,? Math. Z.,188, 253?269 (1985). · Zbl 0535.20028 · doi:10.1007/BF01304213 |
[11] | J.-P. Serre, ?Le problème des groupes de congruence pour SL2,? Ann. Math., II, Ser.92, 489?527 (1970). · Zbl 0239.20063 · doi:10.2307/1970630 |
[12] | W. Thurston, ?The geometry and topology of ?-manifolds,? Lecture Notes. Princeton University Press, Princeton, N.J. (1980). |
[13] | H. Zieschang, E. Vogt, and H.-D. Coldeway, ?Flächen und ebene diskontinuierliche Gruppen,? Lect. Notes Math., Vol. 122, Springer-Verlag, Berlin-Heidelberg-New York (1970). 2nd edn.: Lect. Notes Math., 835 (1980).) · Zbl 0204.24002 |
[14] | R. Zimmert, ?ZurSL2 der ganzen Zahlen eines imaginär-quadratischen Zahlkörpers,? Invent. Math.,19, 73?81 (1973). · Zbl 0254.10019 · doi:10.1007/BF01418852 |
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