A proof of the matrix version of Baker's conjecture in Diophantine approximation

TL;DR

This paper proves that the matrix analogue of the Veronese curve is strongly extremal in Diophantine approximation, confirming a conjecture and advancing understanding of matrix approximation properties.

Contribution

It establishes the strong extremality of the matrix Veronese curve, solving a previously open problem in the field.

Findings

Matrix analogue of the Veronese curve is strongly extremal.

Resolved a question posed by Beresnevich, Kleinbock, and Margulis ('15).

Advances the theory of Diophantine approximation for matrices.

Abstract

We prove that the matrix analogue of the Veronese curve is strongly extremal in the sense of Diophantine approximation, thereby resolving a question posed by Beresnevich, Kleinbock, and Margulis ('15) in the affirmative.