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

Abstract

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

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