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

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  30 July 2018

YANN BUGEAUD Open the ORCID record for YANN BUGEAUD [Opens in a new window]  and
GÜLCAN KEKEÇ Open the ORCID record for GÜLCAN KEKEÇ [Opens in a new window]
YANN BUGEAUD*
Affiliation:
Université de Strasbourg, CNRS, IRMA UMR 7501, 7, rue René Descartes, 67000 Strasbourg, France email bugeaud@math.unistra.fr
GÜLCAN KEKEÇ
Affiliation:
Department of Mathematics, Faculty of Science, Istanbul University, 34134, Vezneciler-Istanbul, Turkey email gulkekec@istanbul.edu.tr
*
✉bugeaud@math.unistra.fr
Rights & Permissions [Opens in a new window]

Abstract

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We give transcendence measures for $p$-adic numbers $\unicode[STIX]{x1D709}$, having good rational (respectively, integer) approximations, that force them to be either $p$-adic $S$-numbers or $p$-adic $T$-numbers.

Keywords

Mahler’s classification of p-adic numbersp-adic S-numberp-adic T-numbertranscendence measure

MSC classification

Primary: 11J61: Approximation in non-Archimedean valuations
Secondary: 11J82: Measures of irrationality and of transcendence
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 203 - 211
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is supported by the Scientific Research Projects Coordination Unit of Istanbul University, project number IRP-52249.

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