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

2023/11/30 by Michael Baake, Baake, Michael, Bustos, Alvaro +2 · 1 citation
Computer Science · Mathematics · #11R18 #37B10 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.18454

openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Point sets of number-theoretic origin, such as the visible lattice points or the k-th power free integers, have interesting geometric and spectral properties and give rise to topological dynamical systems that belong to a large class of subshifts with positive topological entropy. Among them are \cB-free systems in one dimension and their higher-dimensional generalisations, most prominently the k-free integers in algebraic number fields. Here, we extend previous work on quadratic fields to the class of cyclotomic fields. In particular, we discuss their entropy and extended symmetries, with special focus on the interplay between dynamical and number-theoretic notions.

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• Radius-zero Extended Symmetries and Irregular Fibres of ℤ^d-Substitution Subshifts

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