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arXiv · 2202.01596

Simultaneous diophantine approximation for a restricted class of pairs of real numbers

Youssef Lazar
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Abstract

We prove that the Littlewood conjecture is satisfied for a restricted class of pairs $(α,β)$ of badly approximable numbers. We use the localization of the roots of a cubic equation with coefficients depending on the diophantine properties for the considered pair $(α,β)$. The estimates of the roots rely on the properties of the denominators of the convergents of the continued fraction expansion of $α$ and $β$.

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Youssef Lazar. 2025-04-19. Simultaneous diophantine approximation for a restricted class of pairs of real numbers. https://arxiv.org/abs/2202.01596

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