A remark on the set of exactly approximable vectors in the simultaneous case

Abstract

We compute the Hausdorff dimension of the set of ψ \psi -exactly approximable vectors, in the simultaneous case, in dimension strictly larger than 2 2 and for approximating functions ψ \psi with order at infinity less than or equal to − 2 -2 . Our method relies on the analogous result in dimension 1 1 , proved by Yann Bugeaud and Carlos Moreira, and a version of Jarník’s theorem on fibres.