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Values of quadratic forms

✍ Scribed by S. Raghavan

Publisher: John Wiley and Sons
Year: 1977
Tongue: English
Weight: 430 KB
Volume: 30
Category: Article
ISSN: 0010-3640
DOI: 10.1002/cpa.3160300302

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A conjecture of G. L. Watson asserts that the two-sided infimum of the values of a non-homogeneous real indefinite quadratic form in \(n\) variables, obtained when the variables range over all integral values, is an invariant under the signature modulo 8. There is an analogous conjecture by Bambah,

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In this article, we provide the complete answer to a question raised by Kitaoka in his book. (1999, ``Arithmetic of Quadratic Forms,'' Cambridge Univ. Press, Cambridge, UK). More precisely, we prove that A 4 = ( 4) represents all but one and D 4 20[2 1 2 ] represents all but three binary positive ev

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The fundamental theorem on representation-finite quivers in 6 indicates a close connection between the representation type of a quiver and the definiteness of a certain quadratic form. Later a similar connection was discovered in other classification problems of representation theory. It turns out t