Universal octonary diagonal forms over some real quadratic fields.
type: Item
instance of: scholarly article
title: Universal octonary diagonal forms over some real quadratic fields.
zbMATH Open document ID: 1120.11301
author: Byeong Moon Kim
published in: Commentarii Mathematici Helvetici
publication date: 2000-12-12T00:00:00Z
review text: Let \(m=n^2-1\) be a positive square-free integer, \(K=\mathbb Q(\sqrt{m})\) and \({\mathcal O}_K\) be the ring of algebraic integers of \(K.\) Then \(\epsilon = n+\sqrt{m}\) is a fundamental unit of \({\mathcal O}_K\) and is totally positive. The main aim of the paper is to prove that the octonary diagonal form \(x_1^2+x_2^2+x_3^2+x_4^2+\epsilon(x_1^2+x_6^2+x_7^2+x_8^2)\) is universal over \({\mathcal O}_K.\)
reviewed by: Andrzej Sładek
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 11E20
zbMATH DE Number: 1542498
MaRDI profile type: Publication
full work available at URL: s000140050133
OpenAlex ID: W1965091137
DOI: 10.1007/S000140050133
description: scientific article; zbMATH DE number 1542498