Inhomogeneous dual Diophantine approximation on affine subspaces

TL;DR

This paper establishes new convergence and divergence theorems for inhomogeneous dual Diophantine approximation on affine subspaces, extending classical results to more general measure-theoretic contexts.

Contribution

It provides the first comprehensive inhomogeneous Khintchine-Groshev type theorems for dual approximation on affine subspaces, including Hausdorff measure results.

Findings

Proved convergence and divergence cases for inhomogeneous approximation on affine subspaces.

Extended divergence results to Hausdorff measures.

Generalized classical Diophantine approximation theorems to affine subspaces.

Abstract

We prove the convergence and divergence cases of an inhomogeneous Khintchine-Groshev type theorem for dual approximation restricted to affine subspaces in $\mathbb{R} ^n$. The divergence results are proved in the more general context of Hausdorff measures.