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arXiv · 2311.14034

On $\mathfrak{P}$-adic continued fractions with extraneous denominators: some explicit finiteness results

Laura Capuano·Sara Checcoli·Marzio Mula·Lea Terracini
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Abstract

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.

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Laura Capuano, Sara Checcoli, Marzio Mula, Lea Terracini. 2023-11-23. On $\mathfrak{P}$-adic continued fractions with extraneous denominators: some explicit finiteness results. https://doi.org/10.1007/s10231-026-01670-8

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