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Published online by Cambridge University Press: 12 December 2019
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.
Communicated by M. Coons
This research was supported by the Scientific Research Projects Coordination Unit of Istanbul University (project number FUA-2018-31152).