Periodicity and pure periodicity in alternate base systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914664374337536 |
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| author | Masáková, Zuzana Pelantová, Edita |
| author_facet | Masáková, Zuzana Pelantová, Edita |
| contents | We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence of integer bases and the Rényi system with one real base. We focus on the so-called alternate base $B$ given by a purely periodic sequence of real numbers greater than 1. We answer an open question of Charlier et al. on the set of numbers with eventually periodic $B$-expansions. We also investigate for which bases all sufficiently small rationals have a purely periodic $B$-expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodicity and pure periodicity in alternate base systems Masáková, Zuzana Pelantová, Edita Number Theory 11K16, 11R06 We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence of integer bases and the Rényi system with one real base. We focus on the so-called alternate base $B$ given by a purely periodic sequence of real numbers greater than 1. We answer an open question of Charlier et al. on the set of numbers with eventually periodic $B$-expansions. We also investigate for which bases all sufficiently small rationals have a purely periodic $B$-expansion. |
| title | Periodicity and pure periodicity in alternate base systems |
| topic | Number Theory 11K16, 11R06 |
| url | https://arxiv.org/abs/2402.01367 |