On transcendental formal power series over finite fields

KEKEÇ G.

BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, vol.63, no.4, pp.349-357, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 4
  • Publication Date: 2020
  • 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.349-357
  • Keywords: Bundschuh's classification of transcendental formal power series, over finite fields, U-number, lacunary power series, transcendence measure, ALGEBRAIC COEFFICIENTS
  • Istanbul University Affiliated: Yes

Abstract

Let K be a finite field and K(x) be the quotient field of the ring of polynomials in x with coefficients in K. In the field K of formal power series over K, we treat certain lacunary power series with algebraic coefficients in a finite extension of K(x). We show that the values of these series at certain U-1-number arguments are either algebraic over K(x) or U-numbers.