We 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.

中文翻译：

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关于 SPRINDŽUK 对 -ADIC 数的分类

我们将 Sprindžuk 的复数分类带到了现场$\mathbb{Q}_{p}$的$p$-进数。我们建立了几个估计$p$-adic 距离$p$-整数多项式的进根，我们应用它来证明几乎所有$p$-关于 Haar 度量的进数是$p$-adic$\波浪号{S}$- 订单数 1。