On the construction of class fields
type: Item
instance of: scholarly article
title: On the construction of class fields
author: Claus Fieker
author: Tommy Hofmann
author: Carlo Sircana
publication date: 2023-08-02T00:00:00Z
review text: 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].
reviewed by: Hayder R. Hashim
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11Y40
zbMATH DE Number: 7721128
zbMATH Keywords: algorithmic number theory
zbMATH Keywords: class field theory
zbMATH Keywords: class field
MaRDI profile type: Publication
full work available at URL: obs.2019.2.239
OpenAlex ID: W2911370464
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DOI: 10.2140/OBS.2019.2.239
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published in: Open Book Series
description: scientific article; zbMATH DE number 7721128