On \mathfrakP-adic continued fractions with extraneous denominators: some explicit finiteness results

2023/11/23 by Capuano, Laura, Checcoli, Sara, Mula, Marzio +1
#11D88 #11J70 #11Y65 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.14034

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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