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arXiv · 0905.0830

Badly approximable numbers and Littlewood-type problems

Yann Bugeaud·Nikolay Moshchevitin
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Abstract

We establish that the set of pairs $(α, β)$ of real numbers such that $$ \liminf_{q \to + \infty} q \cdot (\log q)^2 \cdot \Vert q α\Vert \cdot \Vert q β\Vert > 0, $$ where $\Vert \cdot \Vert$ 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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Yann Bugeaud, Nikolay Moshchevitin. 2009-05-06. Badly approximable numbers and Littlewood-type problems. https://arxiv.org/abs/0905.0830

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