Metrical results on systems of small linear forms

TL;DR

This paper advances the metric theory of Diophantine approximation for small linear forms by establishing Khintchine-Groshev theorems and Hausdorff measure results without requiring monotonicity of the approximating function.

Contribution

It provides new metric results for small linear forms, extending classical theorems to more general settings without monotonicity constraints.

Findings

Established Khintchine-Groshev theorems for small linear forms.

Generalized Hausdorff measure results in this context.

Removed the monotonicity assumption on the approximating function.

Abstract

In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine-Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function.