On $\mathfrak{P}$-adic continued fractions with extraneous denominators: some explicit finiteness results
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915855251537920 |
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| author | Capuano, Laura Checcoli, Sara Mula, Marzio Terracini, Lea |
| author_facet | Capuano, Laura Checcoli, Sara Mula, Marzio Terracini, Lea |
| contents | Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $\mathfrak P$-adic continued fractions satisfying the finiteness property on $K$ for every prime ideal $\mathfrak P$ of sufficiently large norm. This provides, in particular, a new algorithmic approach to the construction of division chains in number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14034 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $\mathfrak{P}$-adic continued fractions with extraneous denominators: some explicit finiteness results Capuano, Laura Checcoli, Sara Mula, Marzio Terracini, Lea Number Theory 11J70, 11D88, 11Y65 Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $\mathfrak P$-adic continued fractions satisfying the finiteness property on $K$ for every prime ideal $\mathfrak P$ of sufficiently large norm. This provides, in particular, a new algorithmic approach to the construction of division chains in number fields. |
| title | On $\mathfrak{P}$-adic continued fractions with extraneous denominators: some explicit finiteness results |
| topic | Number Theory 11J70, 11D88, 11Y65 |
| url | https://arxiv.org/abs/2311.14034 |