Integral points close to a space curve

TL;DR

This paper derives precise bounds on the number of integer points near scaled space curves with non-zero torsion, advancing understanding of Diophantine approximation in geometric contexts.

Contribution

It provides the first sharp bounds for integral points close to dilated space curves with non-vanishing torsion.

Findings

Established sharp bounds for integral points near space curves.

Extended results to curves with nowhere vanishing torsion.

Enhanced understanding of Diophantine approximation in geometric settings.

Abstract

We establish sharp lower and upper bounds for the number of integral points near dilations of a space curve with nowhere vanishing torsion.