On $$\mathfrak {P}$$-adic continued fractions with extraneous denominators: some explicit finiteness results
Abstract
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 $$\mathfrak {P}$$ P -adic continued fractions satisfying the finiteness property on K for every prime ideal $$\mathfrak {P}$$ P of sufficiently large norm. This provides, in particular, a new algorithmic approach to the construction of division chains in number fields.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Coding theory and cryptography
advanced mathematical theories
Publication details
- Journal / source
- Annali di Matematica Pura ed Applicata (1923 -)
- Publisher
- Springer Science and Business Media LLC
- Volume
- 205
- Issue
- 4
- Pages
- 2259–2286
- Publication date
- 20 February 2026
- Language
- EN