An asymptotics of variance of the lattice points count
The variance of the number of lattice points inside the dilated bounded set rD with random position in R^d 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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