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Pré-Publication, Document De Travail Année : 2005

On the Littlewood conjecture in simultaneous Diophantine approximation

Boris Adamczewski

Résumé

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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Dates et versions

hal-00014577 , version 1 (28-11-2005)

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Boris Adamczewski, Yann Bugeaud. On the Littlewood conjecture in simultaneous Diophantine approximation. 2005. ⟨hal-00014577⟩
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