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

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

2011-05-17

arxiv.org/abs/1105.3495v1

Mathematics

Number Theory

34 pages

Scientific paper

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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