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arXiv · 1105.3495

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

Pierre Le Boudec
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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.

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Pierre Le Boudec. 2011-05-17. Manin's conjecture for a cubic surface with 2A_2+A_1 singularity type. https://doi.org/10.1017/s030500411200031x

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