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This paper considers the asymptotic properties for the spectrum of a positive integer power l of the Laplace-Beltrami operator acting on an n-dimensional torus T. If N(λ) is the number of eigenvalues counted with multiplicity, smaller than a real positive number, we establish a Weyl-type asymptotic formula for the spectral problem of the polyharmonic operators on T, that is, as λ → +∞

One Can Hear the Area of a Torus by Hearing the Eigenvalues of the Polyharmonic Operators