Positive values of inhomogeneous quadratic forms of signature -2
type: Item
instance of: scholarly article
title: Positive values of inhomogeneous quadratic forms of signature -2
zbMATH Open document ID: 0646.10026
DOI: 10.1016/0022-314X(88)90097-2
author: Satish K. Aggarwal
author: Dharma P. Gupta
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Continuing work of \textit{H. Blaney} [J. Lond. Math. Soc. 23, 153-160 (1948; Zbl 0031.20404)] and \textit{R. P. Bambah}, \textit{V. C. Dumir} and \textit{R. J. Hans-Gill} [Colloq. Math. Soc. Janos Bolyai 34, 111-170 (1984; Zbl 0537.10019) and J. Number Theory 16, 403-419 (1983; Zbl 0514.10024)] the authors investigate small positive values of a real indefinite inhomogeneous quadratic form \(Q(x_ 1+r_ 1,...,x_ n+r_ n)\) of signature -2 in integral variables \(x_ i\). They find that any such form of discriminant 1 in \(n\geq 10\) variables assumes values \(\leq 2\cdot 3^{-1/n}\) and that this bound is best possible (this happens to be the same bound as for forms of signature \(+2)\).
Mathematics Subject Classification ID: 11H50
Mathematics Subject Classification ID: 11E16
zbMATH DE Number: 4053732
zbMATH Keywords: minima of forms
zbMATH Keywords: real inhomogeneous quadratic forms
zbMATH Keywords: small positive values
reviewed by: Rainer Schulze-Pillot
MaRDI profile type: Publication
cites work: Q3322183
cites work: On a conjecture of Jackson on non-homogeneous quadratic forms
cites work: Positive values of non-homogeneous indefinite quadratic forms. II
cites work: Indefinite Quadratic Forms in n Variables
cites work: The inhomogeneous minimum of quadratic forms of signature zero
cites work: Q5528787
cites work: Positive values of inhomogeneous quaternary quadratic forms, I
cites work: Positive values of non-homogeneous quaternary quadratic forms
cites work: Small Positive Values of Indefinite Quadratic Forms
cites work: Gaps Between the Values of Quadratic Polynomials
cites work: Q5803363
cites work: VALUES OF QUADRATIC FORMS (I)
cites work: Values of quadratic forms. III
cites work: Indefinite quadratic polynomials
cites work: Q3262865
cites work: Asymmetric Inequalities for Indefinite Quadratic Forms
Recommended article: Q4858629
Recommended article: Positive values of non-homogeneous indefinite quadratic forms of signature 1
Recommended article: Positive values of inhomogeneous quaternary ouadratic forms, II
Recommended article: Positive values of non-homogeneous indefinite quadratic forms of type (2,4)
Recommended article: Positive values of non-homogeneous indefinite quadratic forms. II
Recommended article: Positive values of inhomogeneous indefinite ternary quadratic forms of type \((2,1)\)
Recommended article: Q3128512
Recommended article: Positive values of non-homogeneous indefinite quadratic forms of type (2,5)
Recommended article: Positive values of non-homogeneous indefinite quadratic forms of type \((3,2)\)
Recommended article: The positive values of inhomogeneous ternary quadratic forms
description: scientific article; zbMATH DE number 4053732