Manin's conjecture predicts the asymptotic behavior of the number of rational
points of bounded height on algebraic varieties. For toric varieties, it was
proved by Batyrev and Tschinkel via height zeta functions and an application of
the Poisson formula. An alternative approach to Manin's conjecture via
universal torsors was used so far mainly over the field Q of rational numbers.
In this note, we give a proof of Manin's conjecture over the Gaussian rational
numbers Q(i) and over other imaginary quadratic number fields with class number
1 for the singular toric cubic surface defined by t^3=xyz.Comment: 16 page