Hausdorff dimension of singular vectors in function fields

Noy Soffer Aranov; Taehyeong Kim

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Hausdorff dimension of singular vectors in function fields

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arxiv 2405.11274 v2 pith:VW43GZAW submitted 2024-05-18 math.NT math.DS

Noy Soffer Aranov , Taehyeong Kim This is my paper · ORCID

classification math.NTmath.DS

keywords dimensionfunctionhausdorffvectorsfieldssingularanaloguebound

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abstract

We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of $\varepsilon$-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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