Manin's conjecture for two quartic del Pezzo surfaces with 3A_1 and A_1+A_2 singularity types

Details Manin's conjecture for two quartic del Pezzo surfaces with 3A_1 and A_1+A_2 singularity types Manin's conjecture for two quartic del Pezzo surfaces with 3A_1 and A_1+A_2 singularity types

2010-06-03

arxiv.org/abs/1006.0691v3

Acta Arith. 151 (2012), no. 2, 109-163

Mathematics

Number Theory

Final version

Scientific paper

We prove Manin's conjecture for two del Pezzo surfaces of degree four which
are split over Q and whose singularity types are respectively 3A_1 and A_1+A_2.
For this, we study a certain restricted divisor function and use a result about
the equidistribution of its values in arithmetic progressions. In this task,
Weil's bound for Kloosterman sums plays a key role.

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