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 P-adic continued fractions satisfying the finiteness property on K for every prime ideal P of sufficiently large norm. This provides, in particular, a new algorithmic approach to the construction of division chains in number fields.
On P-adic continued fractions with extraneous denominators: some explicit finiteness results
Checcoli S.;Mula M.
;Terracini L.
2026-01-01
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 P-adic continued fractions satisfying the finiteness property on K for every prime ideal 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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