We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of ε-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].
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Aranov et al. (2024) studied this question.
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