Estimates on counting functions associated to some hyperbolic operators and spectral properties
Abstract
We study the distribution of the eigenvalues of a linear operator associated to a hyperbolic partial differential equation with periodic boundary conditions. Using some recent results concerning the distributions of the values of indefinite quadratic forms at integers, we are able to derive the equidistribution of the eigenvalues relatively to the Lebesgue measure with exact asymptotics. Also we provide an asymptotic lower bound in the rational case.
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