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

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