Badly approximable numbers and Littlewood-type problems

YANN BUGEAUD, NIKOLAY MOSHCHEVITIN

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Source: Crossref

Published: Jan 12, 2011

DOI: 10.1017/s0305004110000605

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Source abstract

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 R 2 . Our proof rests on a method introduced by Peres and Schlag, that we further apply to various Littlewood-type problems.

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