Integral Points Close to Smooth Plane Curves

TL;DR

This paper discusses the problem of counting integral points near smooth plane curves, providing detailed proofs, corrections, and explicit constant values for a theorem related to this area.

Contribution

It offers a detailed exposition and correction of a theorem by Huxley and Sargos on integral points near plane curves, including explicit constant values.

Findings

Corrected an oversight in the original proof.

Provided explicit values for constants in the theorem.

Enhanced understanding of integral points close to smooth plane curves.

Abstract

This is an exposition of a class of problems and results on the number of integral points close to plane curves. We give a detailed proof of a theorem of Huxley and Sargos, following the account of Bordell\`es. Along the way we correct an oversight in the proof, changing some of the explicit values of the constants in the theorem.