Manin's conjecture for a cubic surface with 2A_2+A_1 singularity type

TL;DR

This paper proves Manin's conjecture for a specific cubic surface with singularities, utilizing advanced results on divisor functions and equidistribution in arithmetic progressions.

Contribution

It is the first to establish Manin's conjecture for a cubic surface with the 2A_2+A_1 singularity type, applying deep equidistribution results.

Findings

Confirmed Manin's conjecture for the specified surface

Utilized advanced divisor function equidistribution results

Connected algebraic geometry with analytic number theory techniques

Abstract

We establish Manin's conjecture for a cubic surface split over Q and whose singularity type is 2A_2+A_1. For this, we make use of a deep result about the equidistribution of the values of a certain restricted divisor function in three variables in arithmetic progressions. This result is due to Friedlander and Iwaniec (and was later improved by Heath-Brown) and draws on the work of Deligne.