English

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}
}