An asymptotics of variance of the lattice points count

Details An asymptotics of variance of the lattice points count An asymptotics of variance of the lattice points count

2007-03-14

arxiv.org/abs/math/0703415v3

Mathematics

Metric Geometry

Scientific paper

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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