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Badly approximable numbers and Littlewood-type problems

Published online by Cambridge University Press:  12 January 2011

YANN BUGEAUD  and
NIKOLAY MOSHCHEVITIN
YANN BUGEAUD
Affiliation:
Université de Strasbourg, Mathématiques, 7, rue René Descartes, 67084 Strasbourg, Cedex, France. e-mail: bugeaud@math.unistra.fr
NIKOLAY MOSHCHEVITIN
Affiliation:
Moscow State University, Number Theory, Leninskie Gory 1, Moscow, Russian Federation. e-mail: moshchevitin@rambler.ru
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Abstract

We establish that the set of pairs (α, β) of real numbers such that where ‖ · ‖ denotes the distance to the nearest integer, has full Hausdorff dimension in R2. Our proof rests on a method introduced by Peres and Schlag, that we further apply to various Littlewood-type problems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 2 , March 2011 , pp. 215 - 226
Copyright
Copyright © Cambridge Philosophical Society 2011

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