On the computation of Hilbert class fields
type: Item
instance of: scholarly article
title: On the computation of Hilbert class fields
zbMATH Open document ID: 0910.11058
published in: Journal of Number Theory
publication date: 1998-09-27T00:00:00Z
review text: The authors present an algorithm for construction of \(\Gamma(k)\) the Hilbert class field of \(k\) (unramified algebraic extension with relative Galois group isomorphic to the class group \(Cl_k)\). The method is to compose Kummer extensions using intermediate fields. The idea is to adjoin \({\root p\of {\mu}}\) where \((\mu)\) is a principal ideal which is the \(p\)-power of an ideal of order \(p\). Since each such \(\mu\) can be endowed with (unknown) units, the number of possibilities to test might be astronomically large, but there are tricks for reducing the search. This extraordinary algorithm is available through KASH (KANT).
reviewed by: Harvey Cohn
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11R37
zbMATH DE Number: 1202431
zbMATH Keywords: algorithm
zbMATH Keywords: Hilbert class field
zbMATH Keywords: Kummer extensions
author: Mario Daberkow
author: Michael E. Pohst
describes a project that uses: KANT/KASH
MaRDI profile type: Publication
full work available at URL: jnth.1997.2208
OpenAlex ID: W2049477745
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DOI: 10.1006/JNTH.1997.2208
description: scientific article; zbMATH DE number 1202431