On absolutely friendly measures on ℚ_S^d

2023/12/01 by Datta, Shreyasi, Liu, Justin
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.00758

Abstract

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

Related

• Metric Diophantine approximation and 'absolutely friendly' measures
• Nonseparable growth of the integers supporting a measure
• Approximate super-resolution of positive measures in all dimensions
• Recovering measures from approximate values on balls
• Sets of full measure avoiding Cantor sets