A finiteness condition for complex continued fraction algorithms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917864615706624 |
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| author | Kalle, Charlene Sélley, Fanni M. Thuswaldner, Jörg M. |
| author_facet | Kalle, Charlene Sélley, Fanni M. Thuswaldner, Jörg M. |
| contents | It is desirable that a given continued fraction algorithm is simple in the sense that the possible representations can be characterized in an easy way. In this context the so-called finite range condition plays a prominent role. We show that this condition holds for complex $\boldsymbolα$-Hurwitz algorithms with parameters $\boldsymbolα\in\mathbb{Q}^2$. This is equivalent to the existence of certain finite partitions related to these algorithms and lies at the root of explorations into their Diophantine properties. Our result provides a partial answer to a recent question formulated by Lukyanenko and Vandehey. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18689 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A finiteness condition for complex continued fraction algorithms Kalle, Charlene Sélley, Fanni M. Thuswaldner, Jörg M. Number Theory Dynamical Systems 11J70 It is desirable that a given continued fraction algorithm is simple in the sense that the possible representations can be characterized in an easy way. In this context the so-called finite range condition plays a prominent role. We show that this condition holds for complex $\boldsymbolα$-Hurwitz algorithms with parameters $\boldsymbolα\in\mathbb{Q}^2$. This is equivalent to the existence of certain finite partitions related to these algorithms and lies at the root of explorations into their Diophantine properties. Our result provides a partial answer to a recent question formulated by Lukyanenko and Vandehey. |
| title | A finiteness condition for complex continued fraction algorithms |
| topic | Number Theory Dynamical Systems 11J70 |
| url | https://arxiv.org/abs/2406.18689 |