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math.NT2021
About the value of the two dimensional Levy's constant
Yitwah Cheung, Nicolas Chevallier
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. T…
math.NT2021
The natural extension of the Gauss map and Hermite best approximations
Nicolas Chevallier
Hermite best approximation vectors of a real number were introduced by Lagarias. A nonzero vector (p, q) Z x N is a Hermite best approximation vector of if there exis…
math.NT2021
Gauss lattices and complex continued fractions
Nicolas Chevallier
Our aim is to find a complex continued fraction algorithm finding all the best Diophantine approximations to a complex number. Using the sequence of minimal vectors in a two dimens…