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

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...

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Bibliographic Details
Published inJournal of the Australian Mathematical Society (2001) Vol. 111; no. 2; pp. 221 - 231
Main Authors BUGEAUD, YANN, KEKEÇ, GÜLCAN
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.10.2021
Subjects
Mathematics
roots of an integer polynomial in ℂp
p-adic transcendental numbers
Liouville’s inequality
11J61
11J82
Sprindžuk’s classification of the complex numbers
transcendence measure
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Summary: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.
ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788719000454