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VARIATIONS AROUND A PROBLEM OF MAHLER AND MENDÈS FRANCE

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  25 April 2012

YANN BUGEAUD
YANN BUGEAUD*
Affiliation:
Université de Strasbourg, Mathématiques, 7, rue René Descartes, 67084 Strasbourg, France (email: bugeaud@math.unistra.fr)
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Abstract

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We discuss the following general question and some of its extensions. Let (εk)k≥1 be a sequence with values in {0,1}, which is not ultimately periodic. Define ξ:=∑ k≥1εk/2k and ξ′:=∑ k≥1εk/3k. Let 𝒫 be a property valid for almost all real numbers. Is it true that at least one among ξ and ξ′ satisfies 𝒫?

Keywords

transcendental numbersalgebraic numbersrational approximationnumbers in different bases

MSC classification

Secondary: 11J82: Measures of irrationality and of transcendence
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 1 , February 2012 , pp. 37 - 44
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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