Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

摘要

For given non-zero integers a, b, q we investigate the density of solutions (x; y) ∈ ?~2 to the binary cubic congruence ax~2 + by~3 ≡ 0 mod q, and use it to establish the Manin conjecture for a singular del Pezzo surface of degree 2 defined over ?.