On inhomogeneous diophantine approximation and Hausdorff dimension
Résumé
Let Γ = ZA + Z^n ⊂ R^n be a dense subgroup with rank n + 1 and let ω(A) denote the exponent of uniform simultaneous rational approximation to the point A. We show that for any real number v ≥ ω(A), the Hausdorff dimension of the set B_v of points in R^n which are v-approximable with respect to Γ, is equal to 1/v.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...