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 Zap. Nauchn. Sem. LOMI, 1984, Volume 134, Pages 157–168 (Mi znsl4746)

Small eigenvalues of automorphic Laplacians in spaces of cusp forms

P. G. Zograf

Abstract: The Yang-Yau inequality for $\lambda$, of the Laplace operator of a compact Riemann surface is adapted to the case of a Fucahian group of the first kind. For certain subgroups of the modular group $PSL(2, \mathbb Z)$ be occurenoe of cuspidal representations of complementary series in the regular representations of $PSL(2, \mathbb R)$ is proved. The degree of any non-constant meromorphic function which is automorphic with respect to a congruence subgroup $\Gamma$ of $PSL(2, \mathbb Z)$, is estimated from below in terms of index of $\Gamma$ in $PSL(2, \mathbb Z)$ only.

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Bibliographic databases:
UDC: 511.3+517.43

Citation: P. G. Zograf, “Small eigenvalues of automorphic Laplacians in spaces of cusp forms”, Automorphic functions and number theory. Part II, Zap. Nauchn. Sem. LOMI, 134, "Nauka", Leningrad. Otdel., Leningrad, 1984, 157–168

Citation in format AMSBIB
\Bibitem{Zog84} \by P.~G.~Zograf \paper Small eigenvalues of automorphic Laplacians in spaces of cusp forms \inbook Automorphic functions and number theory. Part~II \serial Zap. Nauchn. Sem. LOMI \yr 1984 \vol 134 \pages 157--168 \publ "Nauka", Leningrad. Otdel. \publaddr Leningrad \mathnet{http://mi.mathnet.ru/znsl4746} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=741858} \zmath{https://zbmath.org/?q=an:0536.10018} 

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This publication is cited in the following articles:
1. Lubotzky A., “Expander Graphs in Pure and Applied Mathematics”, Bull Amer Math Soc, 49:1 (2012), 113–162
2. St. Petersburg Math. J., 26:4 (2015), 593–606