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

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.

preprint2011arXivOpen access
Pierre Le Boudec
math.AGmath.NT
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Pierre Le Boudec

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