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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2311.18454 |
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| _version_ | 1866909618132746240 |
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| author | Baake, Michael Bustos, Alvaro Nickel, Andreas |
| author_facet | Baake, Michael Bustos, Alvaro Nickel, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18454 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $k$-free numbers in cyclotomic fields: entropy, symmetries and topological invariants Baake, Michael Bustos, Alvaro Nickel, Andreas Dynamical Systems Number Theory 37B10, 11R18 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. |
| title | On $k$-free numbers in cyclotomic fields: entropy, symmetries and topological invariants |
| topic | Dynamical Systems Number Theory 37B10, 11R18 |
| url | https://arxiv.org/abs/2311.18454 |