A note on weighted badly approximable linear forms

TL;DR

This paper proves a result in twisted Diophantine approximation using Schmidt games, providing an affirmative answer to a conjecture of Schmidt under certain conditions.

Contribution

It offers a new proof of a conjecture in Diophantine approximation related to weighted badly approximable linear forms using Schmidt game techniques.

Findings

Confirmed a conjecture in twisted Diophantine approximation

Applied Schmidt game methods to linear forms

Extended understanding of badly approximable sets

Abstract

We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give a affirmative answer to the analogue in this setting of a famous conjecture of Schmidt from Diophantine approximation.