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<p>In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions <i>A</i> and <i>B</i> which guarantee that the p-adic continued fraction <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A^{B}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mi>B</mi> </msup> </math></EquationSource> </InlineEquation> is a transcendental number over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation> in the p-adic framework. Furthermore, we give some numerical examples which illustrated the theoretical results.</p>

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Transcendence of some p-adic continued fractions

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Sarra Ahallal,
  • Ali Kacha

摘要

In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions A and B which guarantee that the p-adic continued fraction \(A^{B}\) A B is a transcendental number over \(\mathbb {Q}\) Q in the p-adic framework. Furthermore, we give some numerical examples which illustrated the theoretical results.