Exact Approximation in the Field of Formal Power Series

In this article, we determine the Hausdorff dimension of the set of exactly ψ-approximable vectors over local fields of positive characteristic. This result is the function field analogue of a recent theorem of Bandi and de Saxce in the real setting [BdS25], and extends the main theorem of Zhang [Zha12] to higher dimensions. Our approach adapts the method of Bandi and de Saxce to the ultrametric setting, enabling us to overcome difficulties arising from the failure of the well-separatedness property for rational functions in higher dimensions.