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<p>Let <i>K</i> 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak {P}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">P</mi> </math></EquationSource> </InlineEquation>-adic continued fractions satisfying the finiteness property on <i>K</i> for every prime ideal <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathfrak {P}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">P</mi> </math></EquationSource> </InlineEquation> of sufficiently large norm. This provides, in particular, a new algorithmic approach to the construction of division chains in number fields.</p>

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On \(\mathfrak {P}\)-adic continued fractions with extraneous denominators: some explicit finiteness results

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月20日

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  • Laura Capuano,
  • Sara Checcoli,
  • Marzio Mula,
  • Lea Terracini

摘要

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.