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The density of rational points on a certain singular cubic surface

T. D. Browning
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Abstract

We show that the number of non-trivial rational points of height at most $B$, that lie on the cubic surface $x_1x_2x_3=x_4(x_1+x_2+x_3)^2$, has order of magnitude $B(\log B)^6$. This agrees with the Manin conjecture.

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T. D. Browning. 2005-11-04. The density of rational points on a certain singular cubic surface. https://arxiv.org/abs/math/0404245

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