About Jarník's-type relation in higher dimension

Antoine Marnat (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer [17, 18] and results by D. Roy [13, 14], we show that German's transference inequalities between the two most classical exponents of uniform Diophantine approximation are optimal. Further, we establish that the n uniform exponents of Diophantine approximation in dimension n are algebraically independent. Thus, no Jarník's-type relation holds between them.

Domaines: Théorie des nombres [math.NT]

Antoine Marnat. About Jarník's-type relation in higher dimension. 2016. ⟨hal-01398062⟩