On the Sets of Complex Numbers with Specific Approximation Order

In this talk, we introduce some metric results on the Diophantine approximation of complex numbers. More precisely, let ψ be a positive non-increasing function that tends to zero at infinity, we obtain the Hausdorff and packing dimensions of the sets of ψ-well approximable and ψ-exact approximable complex numbers. These results can be viewed as the analogues of the classical Jarník Theorem in the real case.