Abstract

In the spectral theory of automorphic functions, small eigenvalues (i.e., those lying in the interval [0, 1/4]) of the Laplace operator are of particular interest. In this note we give an upper bound for the number of small eigenvalues of the Laplace operator for noncompact Riemann surfaces, which are quotient spaces of the upper half plane by the action of Fuchsian groups of the first kind, and also of the multiplicity of small eigenvalues.

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