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

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.

We fixed a typo in Proposition 3.6 and updated the affiliations and the bibliography

Cited by in corpus (1)

• Convergence, Finiteness and Periodicity of Several New Algorithms of p-adic Continued Fractions