English

Entropy and diffraction of the $k$-free points in $n$-dimensional lattices

Metric Geometry 2015-05-06 v3 Mathematical Physics math.MP Number Theory

Abstract

We consider the kkth-power-free points in nn-dimensional lattices and explicitly calculate their entropies and diffraction spectra. This is of particular interest since these sets have holes of unbounded inradius.

Keywords

Cite

@article{arxiv.1112.1629,
  title  = {Entropy and diffraction of the $k$-free points in $n$-dimensional lattices},
  author = {Peter A. B. Pleasants and Christian Huck},
  journal= {arXiv preprint arXiv:1112.1629},
  year   = {2015}
}

Comments

27 pages, 2 figures; revised version with new references [7,8,23]; latest version with new Theorem 6 and updated reference [7]