An Explicit Construction of p-adic Um-numbers

KEKEÇ G.

Indian Journal of Pure and Applied Mathematics, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1007/s13226-026-00958-y
  • Journal Name: Indian Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH
  • Keywords: Mahler’s classification of p-adic numbers, p-adic Liouville number, p-adic Um-number, Ruban p-adic continued fraction, Transcendence measure
  • Istanbul University Affiliated: Yes

Abstract

The transcendental p-adic numbers are divided into the three disjoint classes S, T, U and the class U is subdivided into the subclasses Um(m=1,2,3,…) with respect to Mahler’s classification. Using Ruban continued fraction expansions of p-adic Liouville numbers, we prove that integral combinations with algebraic p-adic number coefficients of certain p-adic Liouville numbers are Mahler’s p-adic Um-numbers, where m is the degree of the p-adic algebraic number field determined by these algebraic p-adic number coefficients, and we construct explicit examples to illustrate our results.