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, cilt.69, sa.12, ss.1549-1556, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 12
  • Basım Tarihi: 2016
  • Dergi Adı: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1549-1556
  • Anahtar Kelimeler: formal Laurent series, finite fields, non-archimedean absolute value, liouville numbers, TRANSCENDENCE-MEASURES, APPROXIMATION
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.