On Mahler's Um—numbers in fields of formal power series over finite fields

Can B., KEKEÇ G.

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, vol.67, no.1, pp.79-89, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 1
  • Publication Date: 2024
  • Journal Name: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.79-89
  • Keywords: continued fraction, Mahler's classification of transcendental formal power series over a finite field, transcendence measure, U-number
  • Istanbul University Affiliated: Yes

Abstract

Let K be a finite field, K(x) be the quotient field of the ring of polynomials in x with coefficients in K and K be the field of formal power series over K. In this paper, we treat polynomials whose coefficients belong to a field extension of degree m over K(x). We show that the values of these polynomials at certain U1-numbers in the field K are Um— numbers in K.