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Point sets of number-theoretic origin, such as the visible lattice points orthe $k$-th power free integers, have interesting geometric and spectralproperties and give rise to topological dynamical systems that belong to alarge class of subshifts with positive topological entropy. Among them are$\cB$-free systems in one dimension and their higher-dimensionalgeneralisations, most prominently the $k$-free integers in algebraic numberfields. Here, we extend previous work on quadratic fields to the class ofcyclotomic fields. In particular, we discuss their entropy and extendedsymmetries, with special focus on the interplay between dynamical andnumber-theoretic notions.

On $k$-free numbers in cyclotomic fields: entropy, symmetries and topological invariants