On a certain non-split cubic surface

Abstract

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $$x_0(x_1^2 + x_2^2)=x_3^3$$ with a power-saving error term, which verifies the Manin-Peyre conjectures for this surface.Comment: v2. 18 pages, one author adde