On Manin's conjecture for Ch\^atelet surfaces

TL;DR

This paper proves Manin's conjecture for all Châtelet surfaces over the rational numbers, confirming predicted distribution of rational points.

Contribution

It provides a complete proof of Manin's conjecture specifically for Châtelet surfaces over ield.

Findings

Manin's conjecture is confirmed for all Che2telet surfaces over ield.

The distribution of rational points on these surfaces matches the conjectured asymptotic behavior.

The result completes the classification of rational points for this class of surfaces.

Abstract

We resolve Manin's conjecture for all Ch\^atelet surfaces over $\mathbb{Q}$.