On inhomogeneous diophantine approximation and Hausdorff dimension

Michel Laurent (1)

1 I2M - Institut de Mathématiques de Marseille

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]

Michel Laurent. On inhomogeneous diophantine approximation and Hausdorff dimension. International Journal of Applied Mathematical Sciences, 2012, ⟨10.1007/s10958-012-0658-x⟩. ⟨hal-01262178⟩