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arXiv · 2503.06110

Exact Approximation In The Field Of Formal Series

Aratrika Pandey
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Abstract

In this article, we determine the Hausdorff dimension of the set of exactly $\psi$-approximable vectors over local fields of positive characteristic. This result is the function field analogue of a recent theorem of Bandi and de Saxc\'e in the real setting~\cite{bandi2023hausdorff}, and extends the main theorem of Zhang~\cite{MR2834892} to higher dimensions. Our approach adapts the method of Bandi and de Saxc\'e to the ultrametric setting, enabling us to overcome difficulties arising from the failure of the well-separatedness property for rational functions in higher dimensions.

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Aratrika Pandey. 2025-03-08. Exact Approximation In The Field Of Formal Series. https://arxiv.org/abs/2503.06110

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