Dynamical Properties of k-Free Lattice Points |
| C. Huck and M. Baake
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany |
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| We revisit the visible points of a lattice in Euclidean n-space together with their generalisations, the k-th-power-free points of a lattice, and study the corresponding dynamical system that arises via the closure of the lattice translation orbit. Our analysis extends previous results obtained by Sarnak and by Cellarosi and Sinai for the special case of square-free integers and sheds new light on previous joint work with Peter Pleasants. |
DOI: 10.12693/APhysPolA.126.482 PACS numbers: 61.05.cc, 61.43.-j, 61.44.Br |