About the value of the two dimensional Levy's constant
Abstract
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 \cite{Xieu}.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.01907
 Bibcode:
 2021arXiv210701907C
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Dynamical Systems
 EPrint:
 13 pages, 4 figures