Computing Igusa class polynomials

Details Computing Igusa class polynomials Computing Igusa class polynomials

2009-03-27

arxiv.org/abs/0903.4766v2

Mathematics

Number Theory

30 pages (Updated version: ramification assumptions removed, various minor corrections, and a shorter exposition. For the more

Scientific paper

We give an algorithm that computes the genus-two class polynomials of a primitive quartic CM-field K, and we give a running time bound and a proof of correctness of this algorithm. This is the first proof of correctness and the first 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 Otilde(Delta^(7/2)), where Delta is the discriminant of K.

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