Hausdorff dimension of singular vectors in function fields

Abstract

We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of $\epsilon$-Dirichlet improvable vectors in this setting. This is a function field analogue of the results of Cheung and Chevallier [Duke Math. J. 165 (2016), 2273--2329].

25 pages, Minor errata were corrected