A conjecture of Manin predicts the distribution of -rational points on certain algebraic varieties defined over a number field . In recent years, a method using universal torsors has been successfully applied to several hard special cases of Manin’s conjecture over the field . 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 given by the equation .
"Counting rational points over number fields on a singular cubic surface." Algebra Number Theory 7 (6) 1451 - 1479, 2013. https://doi.org/10.2140/ant.2013.7.1451