ON SPRINDZUK'S CLASSIFICATION OF p-ADIC NUMBERS

Bugeaud Y., Kekec G.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, cilt.111, sa.2, ss.221-231, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 111 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1017/s1446788719000454
  • Dergi Adı: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.221-231
  • Anahtar Kelimeler: Sprindzuk's classification of the complex numbers, p-adic transcendental numbers, transcendence measure, roots of an integer polynomial in Double-struck capital C-p, Liouville's inequality
  • İstanbul Üniversitesi Adresli: Evet

Özet

We carry Sprindzuk's classification of the complex numbers to the field Q(p) of p-adic numbers. We establish several estimates for the p-adic distance between p-adic roots of integer polynomials, which we apply to show that almost all p-adic numbers, with respect to the Haar measure, are p-adic (S) over tilde -numbers of order 1.