This article is cited in 1 paper

Asymptotic behaviour of the spectral function of the Laplace–Beltrami operator for cocompact discrete subgroups of $\operatorname {SL}_2(\mathbb R)$

V. V. Golovchanskii

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: An asymptotic formula, uniform in $z$ and $z'$, is obtained for the spectral function $\theta (z,z',\lambda )$ of the Laplace–Beltrami operator for cocompact discrete subgroups of $\operatorname {SL}_2(\mathbb R)$ with power-law lowering of the order of the remainder.

UDC: 517

MSC: Primary 11F72, 58G25; Secondary 11F25, 32N10, 58G18

Received: 05.10.1995 and 19.02.1998

DOI: 10.4213/sm335

 English version: Sbornik: Mathematics, 1998, 189:7, 977–990

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