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arXiv · 2312.00758

On absolutely friendly measures on $\mathbb{Q}_S^d$

Shreyasi Datta·Justin Liu
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Abstract

In this paper, we extend the work of Pollington and Velani in \cite{PV} to an $S$-arithmetic set-up, where $S$ is a finite set of valuations of $\mathbb{Q}$. In particular, for an `absolutely friendly' measure supported on a compact set in $\mathbb{Q}_S^d$, we give a summation condition on approximating function $\psi$ such that $\mu$ almost no point in the compact set is $\psi$ approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.

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Shreyasi Datta, Justin Liu. 2023-12-01. On absolutely friendly measures on $\mathbb{Q}_S^d$. https://arxiv.org/abs/2312.00758

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