Theorem on best Diophantine approximations for linear forms

TL;DR

This paper presents a new quantitative theorem concerning the degeneracy of the dimension of subspaces spanned by the best Diophantine approximations of a linear form, advancing understanding in number theory.

Contribution

It introduces a novel quantitative result on the degeneracy of the dimension of subspaces related to best Diophantine approximations for linear forms.

Findings

Established a new quantitative bound on degeneracy

Improved understanding of the structure of best Diophantine approximations

Provided insights into the geometry of approximation subspaces

Abstract

We prove a new quantitative result on the degeneracy of the dimension of the subspace spanned by the best Diophantine approximations for a linear form.