Affine congruences and rational points on a certain cubic surface

Abstract

We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q and whose singularity type is D_4. This improves on a result of Browning and answers a problem posed by Tschinkel.

References in corpus (2)

• Singular del Pezzo surfaces whose universal torsors are hypersurfaces
• Manin's conjecture for a cubic surface with 2A_2+A_1 singularity type

Cited by in corpus (3)

• Cox rings of cubic surfaces and Fano threefolds
• On the saturation number for cubic surfaces
• On the saturation number for singular cubic surfaces