ON SPRINDZUK'S CLASSIFICATION OF p-ADIC NUMBERS

Bugeaud Y., Kekec G.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.111, no.2, pp.221-231, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 111 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1017/s1446788719000454
  • Journal Name: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.221-231
  • Keywords: 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
  • Istanbul University Affiliated: Yes

Abstract

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.