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ON MAHLER’S $p$-ADIC $U_{m}$-NUMBERS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  21 August 2012

GÜLCAN KEKEÇ
GÜLCAN KEKEÇ*
Affiliation:
Faculty of Science, Department of Mathematics, Istanbul University, 34134 Vezneciler-Istanbul, Turkey (email: gulkekec@istanbul.edu.tr)
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Abstract

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The aim of this work is to adapt a construction of the so-called $U_{m}$-numbers ($m\gt 1$), which are extended Liouville numbers with respect to algebraic numbers of degree $m$ but not with respect to algebraic numbers of degree less than $m$, to the $p$-adic frame.

Keywords

Mahler’s classification of p-adic numbersp-adic U-numbertranscendence measure

MSC classification

Secondary: 11J61: Approximation in non-Archimedean valuations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 44 - 50
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

References

[1]Alnıaçık, K., Avcı, Y. & Bugeaud, Y., ‘On $U_{m}$-numbers with small transcendence measure’, Acta Math. Hungar. 99(4) (2003), 271–277.CrossRefGoogle Scholar
[2]Bugeaud, Y., Approximation by Algebraic Numbers, Cambridge Tracts in Mathematics, 160 (Cambridge University Press, Cambridge, 2004).CrossRefGoogle Scholar
[3]Mahler, K., ‘Über eine Klasseneinteilung der $p$-adischen Zahlen’, Mathematica (Leiden) 3 (1935), 177–185.Google Scholar
[4]Pejkovic, T., Polynomial Root Separation and Applications, PhD Thesis (Université de Strasbourg, Strasbourg, 2012).Google Scholar
[5]Schlickewei, H. P., ‘$p$-adic $T$-numbers do exist’, Acta Arith. 39 (1981), 181–191.CrossRefGoogle Scholar