Representations of binary forms by certain quinary positive integral quadratic forms
type: Item
instance of: scholarly article
title: Representations of binary forms by certain quinary positive integral quadratic forms
zbMATH Open document ID: 1003.11010
author: Myung Hwan Kim
author: Ja Kyung Koo
author: Byeong-Kweon Oh
published in: Journal of Number Theory
publication date: 2002-06-04T00:00:00Z
review text: Let \(f:= 2(\sum_{i=1}^4 x_i^2+ 2x_5^2- x_1x_2- x_2x_3- x_3x_4)\) and \(g:= 2(\sum_{i=1}^4 x_i^2+ 3x_5^2- x_1x_2- x_1x_3- x_1x_4- x_1x_5+ x_2x_5+ x_3x_5)\). It is proved that \(f\) represents all but one and \(g\) represents all but three binary positive even \(\mathbb{Z}\)-lattices. (This answers a question by Kitaoka.) Furthermore representations of binary quadratic forms by quinary quadratic forms in certain positive even 2-universal genera of class number 2 are investigated.
Mathematics Subject Classification ID: 11E20
Mathematics Subject Classification ID: 11E25
zbMATH DE Number: 1749024
zbMATH Keywords: positive definite quadratic forms
zbMATH Keywords: representations of binary quadratic forms
zbMATH Keywords: quinary quadratic forms
reviewed by: Meinhard Peters
MaRDI profile type: Publication
OpenAlex ID: W1991984767
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DOI: 10.1006/JNTH.2000.2631
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description: scientific article; zbMATH DE number 1749024