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The density of rational points on Cayley's cubic surface

D. R. Heath-Brown
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Abstract

The Cayley cubic surface is given by the equation sum_{i=1}^4 X_i^{-1}=0. We show that the number of non-trivial primitive integer points of size at most B is of exact order B(log B)^6, as predicted by Manin's conjecture.

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D. R. Heath-Brown. 2002-10-21. The density of rational points on Cayley's cubic surface. https://arxiv.org/abs/math/0210333

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