AN ALGORITHM FOR COMPUTING THE STICKELBERGER IDEAL FOR MULTIQUADRATIC NUMBER FIELDS

Abstract

We present an algorithm for computing the Stickelberger ideal for multiquadratic fields K = Q(√d1,√d2, . . . , √dn), where the integers di ≡ 1 mod 4 for i ∈ {1, . . . , n} or dj ≡ 2 mod 8 for one j ∈ {1, . . . , n}; all di’s are pairwise co-prime and squarefree. Our result is based on the paper of Kuˇcera [J. Number Theory, no. 56, 1996]. The algorithm we present works in time O(lg ∆K • 2n• poly(n)), where ∆K is the discriminant of K. As an interesting application, we show a connection between Stickelberger ideal and the class number of a multiquadratic field