On the Computation of Class Polynomials with “Thetanullwerte” and Its Applications to the Unit Group Computation

Abstract

The classical class invariants of Weber are introduced as quotients of Thetanullwerte, enabling the computation of these invariants more efficiently than as quotients of values of the Dedekind η-function. We show also how to compute the unit group of suitable ring class fields by proving the fact that most of the invariants introduced by Weber are actually units in the corresponding ring class fields.