ON THE VALUES OF SOME POWER SERIES IN THE FIELD OF FORMAL LAURENT SERIES OVER A FINITE FIELD

Caliskan F.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, vol.69, no.12, pp.1549-1556, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 12
  • Publication Date: 2016
  • Journal Name: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1549-1556
  • Keywords: formal Laurent series, finite fields, non-archimedean absolute value, liouville numbers, TRANSCENDENCE-MEASURES, APPROXIMATION
  • Istanbul University Affiliated: Yes

Abstract

In 1932, Mahler introduced a classification of transcendental numbers that pertained to both complex and p-adic numbers. Bundschuh then extended Mahler's classification so that it included the field of formal Laurent series over a finite field. Herein, we show that the values of some power series in field of formal Laurent series over a finite field are either Liouville numbers, or they can be included in the quotient field of the polynomial ring on the finite field for Liouville number arguments under certain conditions.