Linear growth for Ch\^atelet surfaces

TL;DR

This paper establishes an upper bound on the expected number of rational points of bounded height on Châtelet surfaces over the rationals, contributing to the understanding of rational point distribution.

Contribution

It provides a new upper bound for the count of rational points on Châtelet surfaces, advancing the theoretical understanding of their distribution.

Findings

Upper bound on rational points of bounded height

Improved understanding of Châtelet surface rational points

Theoretical framework for counting rational points

Abstract

An upper bound of the expected order of magnitude is established for the number of rational points of bounded height on Ch\^atelet surfaces defined over the rationals.