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

Author:

Fregoli Reynold

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.

Publisher

American Mathematical Society (AMS)

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