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Fuchsian groups and small eigenvalues of the Laplace operator. (English) Zbl 0565.10021

Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 122, 24-29 (Russian) (1982; Zbl 0536.10017).

MSC:

11F03 Modular and automorphic functions
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
35P99 Spectral theory and eigenvalue problems for partial differential equations
11F70 Representation-theoretic methods; automorphic representations over local and global fields
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References:

[1] A. B. Venkov, ?Spectral theory of automorphic functions, the Selberg zeta-function, and some problems of analytic number theory and mathematical physics,? Usp. Mat. Nauk,34, No. 3, 69?135 (1979). · Zbl 0437.10012
[2] I. M. Gel’fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Theory of Representations and Automorphic Functions [in Russian], Moscow (1966).
[3] P. Buser, ?Riemannsche Flächen mit Eigenwerten in (0, 1/4),? Comment. Math. Helv.,52, No. 1, 25?34 (1977). · Zbl 0348.53027 · doi:10.1007/BF02567355
[4] A. Selberg, ?Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series,? J. Indian Math. Soc.,20, Nos. 1?3, 47?87 (1956). · Zbl 0072.08201
[5] S.-Y. Cheng, ?Eigenfunctions and nodal sets,? Comment. Math. Helv.,51, No. 1, 43?55 (1976). · Zbl 0334.35022 · doi:10.1007/BF02568142
[6] L. D. Faddeev, ?Expansion in eigenfunctions of the Laplace operator on a fundamental domain of a discrete group on the Lobachevskii plane,? Tr. Mosk. Mat. Obshch.,17, 323?349 (1967). · Zbl 0201.41601
[7] G. Besson, ?Sur la multiplicite de la premiere valeur propre des surfaces riemanniennes,? Ann. Inst. Fourier,30, No. 1, 109?128 (1980). · Zbl 0417.30033 · doi:10.5802/aif.777
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