Proximality of multidimensional $\mathscr{B}$-free systems

TL;DR

This paper characterizes when multidimensional $B$-free systems, associated with number fields and lattices, exhibit proximality, extending understanding of their dynamical behavior in higher dimensions.

Contribution

It provides a characterization of proximality for multidimensional $B$-free systems in the context of number fields and lattices, a novel extension of previous one-dimensional results.

Findings

Proximality criteria for multidimensional $B$-free systems.

Extension of $B$-free system analysis to number fields.

Insights into the dynamical properties of these systems.

Abstract

We characterize proximality of multidimensional $\mathscr{B}$-free systems in the case of number fields and lattices in $\mathbb{Z}^m$, $m\geq2$.