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

We compute the Hausdorff dimension of the set of ψ -exactly approximable vectors, in the simultaneous case, in dimension strictly larger than 2 2 and for approximating functions ψ 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.