Points of bounded height on quintic del Pezzo surfaces over the rational numbers

TL;DR

This paper provides a concise and elementary proof of Manin's conjecture concerning the distribution of rational points of bounded height on split smooth quintic del Pezzo surfaces over the rationals.

Contribution

It offers a simplified and accessible proof of Manin's conjecture for this class of algebraic surfaces, expanding understanding in arithmetic geometry.

Findings

Proof confirms Manin's conjecture for the specified surfaces

Simplifies previous approaches to the conjecture

Enhances understanding of rational points on del Pezzo surfaces

Abstract

We give a relatively short and elementary proof of Manin's conjecture for split smooth quintic del Pezzo surfaces over the rational numbers.