On the construction of class fields
In the paper, the authors discuss improvements to the computation of ray class groups, congruence subgroups and class fields, which are fundamental building blocks of constructive class field theory. More precisely, they describe new methods for computing class fields with an emphasis on the problem of tabulating extensions of number fields. However, their strategy is the same as in [\textit{H. Cohen} et al., Math. Comput. 67, No. 222, 773--795 (1998; Zbl 0929.11064)] and [\textit{M. Daberkow} and \textit{M. Pohst}, in: Proceedings of the 1995 international symposium on symbolic and algebraic computation, ISSAC '95, Montreal, Canada, July 10--12, 1995. New York, NY: ACM Press. 68--76 (1995; Zbl 0930.11089)], they show how the individual steps can be improved tremendously. As an application and to illustrate the power of their new techniques, they find new fields with minimal discriminant having prescribed Galois group and signature. For the entire collection see [Zbl 1416.11009].
scientific article; zbMATH DE number 7721128
scientific article