ON SPRINDZUK'S CLASSIFICATION OF p-ADIC NUMBERS

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.