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arXiv · 2105.12570

On the finiteness of $\mathfrak{P}$-adic continued fractions for number fields

Laura Capuano·Nadir Murru·Lea Terracini
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Abstract

For a prime ideal $\mathfrak{P}$ of the ring of integers of a number field $K$, we give a general definition of $\mathfrak{P}$-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 $\alpha\in K$ admits a finite $\mathfrak{P}$-adic continued fraction expansion for all but finitely many $\mathfrak{P}$, addressing a similar problem posed by Rosen in the archimedean setting.

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Laura Capuano, Nadir Murru, Lea Terracini. 2021-05-26. On the finiteness of $\mathfrak{P}$-adic continued fractions for number fields. https://arxiv.org/abs/2105.12570

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