Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights

TL;DR

This paper proves a zero-full law for the Hausdorff measure of inhomogeneous Dirichlet non-improvable affine forms with weights, addressing a question from recent mathematical research.

Contribution

It establishes a zero-full law for Hausdorff measure in the context of inhomogeneous affine forms with weights, under certain decay conditions, advancing the understanding of Diophantine approximation.

Findings

Established a zero-full law for Hausdorff measure

Answered a question posed by Kim and Kim (2022)

Provided conditions under which the law holds

Abstract

Under a reasonable decay assumption on the approximating function, we establish a zero-full law for the Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights, thereby answering a question posed by Kim and Kim (\S 5.3, Adv. Math., 2022).