volume 170, issue 2, P375-403 1995
DOI: 10.1007/bf02108334
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Abstract:We consider the Weyl asymptotic formula for eigenvalues of the Laplace-Beltrami operator on a two-dimensional torus Q with a Liouville metric which is in a sense the most general case of an integrable metric. We prove that if the surface Q is non-degenerate then the remainder term n(R) has the form n(R) -R ι/2 Θ(R), where Θ(R) is an almost periodic function of the Besicovitch class B ι , and the Fourier amplitudes and the Fourier frequencies of Θ(R) can be expressed via lengths of closed geodesies on Q and oth…

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