CONSTRUCTION OF INTEGRAL BASES IN ABELIAN FIELD-EXTENSIONS OF IMAGINARY QUADRATIC NUMBER-FIELDS

[摘要] Let K be an imaginary quadratic number field and Rf the ring class field modulo f over K, f is-an-element-of N. Let O(f) denote the order of conductor f in K and let A subset-or-equal-to K be a proper O(f)-ideal. Using the methods of R. Schertz (J. Reine Angew. Math. 398, 1989, 105-129) a relative integral basis is constructed for R(f)(tau(xi \ A))/R(f), (xi is-an-element-of K\A. Here tau denotes the Weber function. The factorization into a product of prime ideals of the singular values phi(xi \ A) of the Siegel function is completely determined. (C) 1994 Academic Press, Inc.

[发布日期] 1994-03-01