An asymptotics of variance of the lattice points count
Metric Geometry
2018-07-04 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0703415,
title = {An asymptotics of variance of the lattice points count},
author = {Jirí Janácek},
journal= {arXiv preprint arXiv:math/0703415},
year = {2018}
}