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, cilt.67, sa.1, ss.79-89, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 1
  • Basım Tarihi: 2024
  • Dergi Adı: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.79-89
  • Anahtar Kelimeler: continued fraction, Mahler's classification of transcendental formal power series over a finite field, transcendence measure, U-number
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.