Computing Igusa class polynomials
We give an algorithm that computes the genus-two class polynomials of a primitive quartic CM-eld K, and we give a running time bound and a proof of correctness of this algorithm. This is the rst proof of correctness and the rst running time bound of any algorithm that computes these polynomials. Our algorithm is based on the complex analytic method of Spallek and van Wamelen and runs in time e O( 7=2 ), where is the discriminant of K.