On the finiteness of \mathfrakP-adic continued fractions for number fields

2021/05/26 by Laura Capuano, Capuano, Laura, Nadir Murru +3
Mathematics · #11D88 #11J70 #11J72 #11Y65 #Advanced Topology and Set Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2105.12570

openalex publication_date 2021/05/26 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28

Abstract

For a prime ideal \mathfrakP of the ring of integers of a number field K, we give a general definition of \mathfrakP-adic continued fraction, which also includes classical definitions of continued fractions in the field of p--adic numbers. We give some necessary and sufficient conditions on K ensuring that every α∈ K admits a finite \mathfrakP-adic continued fraction expansion for all but finitely many \mathfrakP, addressing a similar problem posed by Rosen in the archimedean setting.

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