An asymptotics of variance of the lattice points count
Abstract
The variance of the number of lattice points inside the dilated bounded set rD with random position in Rd has asymptotics r(d-1) if the rotational quadratic average of the modulus of the Fourier transform of the set is O(r(-d-1)). The asymptotics follows from a Wiener's Tauberian theorem.
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