Units in families of totally complex algebraic number fields
type: Item
instance of: scholarly article
title: Units in families of totally complex algebraic number fields
zbMATH Open document ID: 1133.11061
DOI: 10.1155/S0161171204312470
author: L. Ya. Vulakh
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/53857
review text: In this particularly well written work, the author applies a multidimensional continued fraction algorithm to determine systems of fundamental units in certain families of totally complex algebraic number fields, of degrees four, six and eight. The algorithm is an analog of one given in the author's paper [Trans. Am. Math. Soc. 356, No. 6, 2325--2348 (2004; Zbl 1055.11065)], and here determines the units of interest by way of determining a fundamental domain for the action of \(\text{GL}_n(\mathcal O_K)/\mu_K\) acting on the Hermitian symmetric space \(\text{SL}_n(\mathbb C)/\text{SU}(n)\), where \(\mathcal O_K\) is the ring of integers of the number field at hand, \(\mu_K\) is the group of roots of unity in \(\mathcal O_K\).
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 2171600
zbMATH Keywords: computing units
zbMATH Keywords: multidimensional continued fractions
reviewed by: Thomas A. Schmidt
MaRDI profile type: Publication
OpenAlex ID: W2166656945
description: scientific article; zbMATH DE number 2171600