ON MAHLER'S CLASSIFICATION OF FORMAL POWER SERIES OVER A FINITE FIELD

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Kekec G.

MATHEMATICA SLOVACA, vol.72, no.1, pp.265-273, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1515/ms-2022-0017
  • Journal Name: MATHEMATICA SLOVACA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.265-273
  • Keywords: Mahler's classification of formal power series over a finite field, U-number, transcendence measure, T-NUMBERS
  • Open Archive Collection: AVESIS Open Access Collection
  • Istanbul University Affiliated: Yes

Abstract

Let K be a finite field, K(x) be the field of rational functions in x over K and K be the field of formal power series over K. We show that under certain conditions integral combinations with algebraic formal power series coefficients of a U-1-number in K are U-m-numbers in K, where m is the degree of the algebraic extension of K(x), determined by these algebraic formal power series coefficients.