Exact Approximation In The Field Of Formal Series

In this article, we prove a lower bound for the Hausdorff dimension of the set of exactly $\psi$-approximable vectors with values in a local field of positive characteristic. This is the analogue of the corresponding theorem of Bandi and de Saxc'e on reals \cite{bandi2023hausdorff} and is a higher-dimensional version of a theorem of Zhang \cite{MR2834892}.

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Journal
ArXiv.org
Published
2025-03-08
Primary Topic
Mathematical Dynamics and Fractals
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article
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article

Exact Approximation In The Field Of Formal Series

ArXiv.org
Mathematical Dynamics and Fractals
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Exact Approximation In The Field Of Formal Series

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Abstract

In this article, we prove a lower bound for the Hausdorff dimension of the set of exactly $\psi$-approximable vectors with values in a local field of positive characteristic. This is the analogue of the corresponding theorem of Bandi and de Saxc'e on reals \cite{bandi2023hausdorff} and is a higher-dimensional version of a theorem of Zhang \cite{MR2834892}.

ArXiv.org
Openalex Percentile: Top 45%
Mathematical Dynamics and Fractals
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Exact Approximation In The Field Of Formal Series · ArXiv.org (2025) | TGRS Research Map | TGRS