On the Littlewood conjecture in simultaneous Diophantine approximation

Boris Adamczewski; Yann Bugeaud

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On the Littlewood conjecture in simultaneous Diophantine approximation

Boris Adamczewski·Yann Bugeaud

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Abstract

For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum many real numbers $\beta$ with bounded partial quotients for which the pair $(\alpha, \beta)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.

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Boris Adamczewski, Yann Bugeaud. 2005-11-28. On the Littlewood conjecture in simultaneous Diophantine approximation. https://arxiv.org/abs/math/0511678

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