Construction of Integral Bases in Abelian Field-Extensions of Imaginary Quadratic Number-Fields Original Research Article

Let K be an imaginary quadratic number field and Rf the ring class field modulo f over K, f set membership, variant image. Let imagef denote the order of conductor f in K and let image subset of or equal to K be a proper imagef-ideal. Using the methods of R. Schertz (J. Reine Angew. Math. 398, 1989, 105-129) a relative integral basis is constructed for Rf(τ(ξ image))/Rf, (ξ set membership, variant K\image. Here τ denotes the Weber function. The factorization into a product of prime ideals of the singular values φ(ξ image) of the Siegel function is completely determined.