ON SPRINDŽUK’S CLASSIFICATION OF -ADIC NUMBERS

Abstract

AbstractWe carry Sprindžuk’s classification of the complex numbers to the field $\mathbb{Q}_{p}$ 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 $\tilde{S}$-numbers of order 1.