Simultaneous two-dimensional best Diophantine approximations in the Euclidean norm

TL;DR

This paper establishes a new lower bound on the growth rate of the best two-dimensional Diophantine approximations measured using the Euclidean norm, advancing understanding of approximation quality.

Contribution

It provides a novel lower bound for the exponent of growth in two-dimensional Diophantine approximation under Euclidean norm, improving previous results.

Findings

New lower bound for growth exponent established

Enhanced understanding of Diophantine approximation in two dimensions

Results applicable to Euclidean norm-based approximation

Abstract

We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.