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arXiv · 2107.01907

About the value of the two dimensional Levy's constant

Yitwah Cheung·Nicolas Chevallier
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Abstract

We give a numerical approximation of the L\'evy constant on the growth of the denominators of the best Diophantine approximations in dimension 2 with respect to the euclidean norm. This constant is expressed as an integral on a surface of dimension 7. We reduce the computation of this integral to a triple integral, whose numerical evaluation was carried out in \cite{Xieu}.

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Yitwah Cheung, Nicolas Chevallier. 2021-07-05. About the value of the two dimensional Levy's constant. https://arxiv.org/abs/2107.01907

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