On the Exact Fourier Dimension of Sets of Well-Approximable Matrices

Abstract

We compute the exact Fourier dimension of the set of $\Psi$-well-approximable $m\times n$ matrices (and the set of $\Psi$-well-approximable numbers) in the homogeneous and inhomogeneous cases for any approximation function $\Psi$ satisfying ${\sum }_{q\in {\mathbb{Z}}^n}\Psi (q{)}^m<\infty$.