• Corpus ID: 235731645

About the value of the two dimensional Levy's constant

@inproceedings{Cheung2021AboutTV,
  title={About the value of the two dimensional Levy's constant},
  author={Yitwah Cheung and Nicolas Chevallier},
  year={2021}
}
We give a numerical approximation of the Lévy 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 [3]. 

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Levy-Khintchin Theorem for best simultaneous Diophantine approximations
We extend two results about the ordinary continued fraction expansion to best simultaneous Diophantine approximations of vectors or matrices. The first is Levy-Khintchin Theorem about the almost sure
Lectures on the Geometry of Numbers
I Minkowski's Two Theorems.- Lecture I.- Lecture II.- Lecture III.- Lecture IV.- II Linear Inequalities.- Lecture V.- Lecture VI.- Lecture VII.- Lecture VIII.- Lecture IX.- III Theory of Reduction.-