# Counting rational points over number fields on a singular cubic surface

@article{Frei2012CountingRP, title={Counting rational points over number fields on a singular cubic surface}, author={Christopher Frei}, journal={arXiv: Number Theory}, year={2012} }

A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successfully applied to several hard special cases of Manin's conjecture over the field Q of rational numbers. Combining this method with techniques developed by Schanuel, we give a proof of Manin's conjecture over arbitrary number fields for the singular cubic surface S given by the equation w^3 = x y z.

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