Equations of the Cayley Surface

The density of rational points on Cayley's cubic surface

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.

The saturation number for Cayley's cubic surface

We investigate the density of rational points on Cayley's cubic surface whose coordinates have few prime factors. The key tools used are the circle method and universal torsors.

Counting rational points on the Cayley ruled cubic

We count rational points of bounded height on the Cayley ruled cubic surface and interpret the result in the context of general conjectures due to Batyrev and Tschinkel.

关于向量分拆约化的Sylvester程序与Cayley算法

On the Sylvester program and Cayley algorithm for vector partition reduction

针对向量分拆约化的Sylvester程序，本文修改了原始Cayley算法以适配其系数条件不满足的情形，并将结果推广到任意数量的丢番图方程，完成向量分拆向标量分拆组合的约化。

关于双分拆的 Cayley 算法

On Cayley algorithm for double partition

针对双分拆问题中 Cayley 原始算法因条件不满足而失效的情况，本文提出其修改版本，以完成向标量分拆之和的归约。

On the saturation number for cubic surfaces

We investigate the density of rational points on the Fermat cubic surface and the Cayley cubic surface whose coordinates have few prime factors. The key tools used are the weighted sieve, the circle method and universal torsors.