Rational points close to non-singular algebraic curves

TL;DR

This paper investigates how densely rational points are distributed near non-singular algebraic curves by analyzing solutions to specific Diophantine inequalities involving ternary forms.

Contribution

It provides new insights into the distribution of rational points close to algebraic curves through the study of Diophantine inequalities involving ternary forms.

Findings

Density results for rational points near algebraic curves

Quantitative bounds on solutions to Diophantine inequalities

Enhanced understanding of rational approximation to algebraic curves

Abstract

We study the density of solutions to Diophantine inequalities involving non-singular ternary forms, or equivalently, the density of rational points close to non-singular plane algebraic curves.