Vol. 2, 2019

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On the construction of class fields

Claus Fieker, Tommy Hofmann and Carlo Sircana

Vol. 2 (2019), No. 1, 239–255
Abstract

Class field theory is an important tool in number theory. We discuss improvements to the computation of ray class groups, congruence subgroups and class fields, which are fundamental building blocks of constructive class field theory. As an application and to illustrate the power of our new techniques, we find new fields with minimal discriminant having prescribed Galois group and signature.

Keywords
algorithmic number theory, class field theory, class field
Mathematical Subject Classification 2010
Primary: 11R37, 11Y40
Milestones
Received: 2 March 2018
Revised: 28 August 2018
Accepted: 9 September 2018
Published: 13 February 2019
Authors
Claus Fieker
Fachbereich Mathematik
Technische Universität Kaiserslautern
Kaiserslautern
Germany
Tommy Hofmann
Fachbereich Mathematik
Technische Universität Kaiserslautern
Kaiserslautern
Germany
Carlo Sircana
Fachbereich Mathematik
Technische Universität Kaiserslautern
Kaiserslautern
Germany