• Transcendence of some power series for Liouville number arguments

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    • Keywords


      Mahler and Koksma classification; Liouville number; algebraic number field; $p$-adic number

    • Abstract


      In this paper, we prove that some power series with rational coefficients take either values of rational numbers or transcendental numbers for the arguments from the set of Liouville numbers under certain conditions in the field of complex numbers. We then apply this result to an algebraic number field. In addition, we establish the $p$-adic analogues of these results and show that these results have analogues in the field of $p$-adic numbers.

    • Author Affiliations



      1. Department of Mathematics, Faculty of Science, Istanbul University, Vezneciler, Fatih, 34134 Istanbul, Turkey
    • Dates

  • Proceedings – Mathematical Sciences | News

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