Ideal composition in quadratic fields: from Bhargava to Gauss
type: Item
instance of: scholarly article
title: Ideal composition in quadratic fields: from Bhargava to Gauss
zbMATH Open document ID: 1275.11139
author: Duncan A. Buell
published in: The Ramanujan Journal
publication date: 2013-01-02T00:00:00Z
review text: \textit{M. Bhargava} [Ann. Math. (2) 159, No. 1, 217--250 (2004; Zbl 1072.11078)] has given a new interpretation to Gauss composition of binary quadratic forms; thus the classical methods of composition also provide methods for computing the Bhargava cubes associated to a triple of binary quadratic forms. In this article, Buell shows how to determine Bhargava's cubes using Arndt's method of composition [\textit{F. Arndt}, J. Reine Angew. Math. 56, 64--71 (1859; ERAM 056.1473cj)].
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 6120467
zbMATH Keywords: quadratic number fields
zbMATH Keywords: Gauss composition
zbMATH Keywords: binary quadratic forms
zbMATH Keywords: class group
zbMATH Keywords: Bhargava cubes
MaRDI profile type: Publication
full work available at URL: s11139-012-9400-z
OpenAlex ID: W2026526618
cites work: Higher composition laws. I: A new view on Gauss composition, and quadratic generalizations
cites work: Higher composition laws. II: On cubic analogues of Gauss composition
cites work: Higher composition laws. III: The parametrization of quartic rings
cites work: Binary quadratic forms. An algorithmic approach
cites work: Q4693156
DOI: 10.1007/S11139-012-9400-Z
description: scientific article; zbMATH DE number 6120467