A Groshev Theorem for Small Linear Forms

TL;DR

This paper extends the classical Khintchine-Groshev theorem to small linear forms, establishing conditions under which the approximation error remains small for a single linear form with a slowly decreasing error function.

Contribution

It provides a new analogue of the Khintchine-Groshev theorem specifically for small linear forms with slowly decreasing error functions.

Findings

Established a Groshev-type theorem for small linear forms.

Identified conditions for approximation errors with slowly decreasing functions.

Extended classical Diophantine approximation results to new settings.

Abstract

In this paper the absolute value or distance from the origin analogue of the classical Khintchine-Groshev theorem is established for a single linear form with a `slowly decreasing' error function.