Inhomogeneous approximation by coprime integers

TL;DR

This paper improves the approximation exponent in inhomogeneous Diophantine approximation with coprime integers from 1/2 to nearly 1, advancing understanding of approximation quality.

Contribution

It provides a new theorem that enhances the known bounds for inhomogeneous approximation by coprime integers, refining previous results.

Findings

Improves the approximation exponent from 1/2 to 1-epsilon for any epsilon>0.

Establishes a new main theorem in inhomogeneous Diophantine approximation.

Offers a corollary that strengthens existing approximation bounds.

Abstract

This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. As a corollary of our main theorem we obtain an improvement of the best known exponent of approximation in this problem, from 1/2 to 1-epsilon, for any epsilon>0.