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 whose singularity type is . This improves on a result of Browning and answers a problem posed by Tschinkel.
"Affine congruences and rational points on a certain cubic surface." Algebra Number Theory 8 (5) 1259 - 1296, 2014. https://doi.org/10.2140/ant.2014.8.1259