A note on rational points near planar curves

TL;DR

This paper proves a conjectured asymptotic formula for counting rational points near planar curves, confirming a key prediction in the field under natural assumptions.

Contribution

It establishes the conjectured asymptotic formula for the number of rational points close to planar curves, advancing understanding in Diophantine approximation.

Findings

Confirmed the conjectured asymptotic formula

Provided bounds of the correct order of magnitude

Enhanced understanding of rational points near curves

Abstract

Under fairly natural assumptions, Huang counted the number of rational points lying close to an arc of a planar curve. He obtained upper and lower bounds of the correct order of magnitude, and conjectured an asymptotic formula. In this note, we establish the conjectured asymptotic formula.