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ON SPRINDŽUK’S CLASSIFICATION OF $p$-ADIC NUMBERS

Published online by Cambridge University Press:  12 December 2019

YANN BUGEAUD
Affiliation:
Université de Strasbourg, CNRS, IRMA UMR 7501, 7, rue René Descartes, 67000Strasbourg, France e-mail: yann.bugeaud@math.unistra.fr
GÜLCAN KEKEÇ
Affiliation:
Istanbul University, Faculty of Science, Department of Mathematics, 34134Vezneciler, Istanbul, Turkey e-mail: gulkekec@istanbul.edu.tr

Abstract

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.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by M. Coons

This research was supported by the Scientific Research Projects Coordination Unit of Istanbul University (project number FUA-2018-31152).

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