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

Counting rational points over number fields on a singular cubic surface