English

Hausdorff dimension of singular vectors in function fields

Number Theory 2024-12-06 v2 Dynamical Systems

Abstract

We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of ε\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].

Keywords

Cite

@article{arxiv.2405.11274,
  title  = {Hausdorff dimension of singular vectors in function fields},
  author = {Noy Soffer Aranov and Taehyeong Kim},
  journal= {arXiv preprint arXiv:2405.11274},
  year   = {2024}
}

Comments

25 pages, Minor errata were corrected

R2 v1 2026-06-28T16:31:50.222Z