Orthogonal splitting and class numbers of quadratic forms
type: Item
instance of: scholarly article
title: Orthogonal splitting and class numbers of quadratic forms
zbMATH Open document ID: 0268.10009
DOI: 10.1016/0022-314X(73)90034-6
author: Larry J. Gerstein
published in: Journal of Number Theory
publication date: 1973-01-01T00:00:00Z
review text: The author's main result may be explained as follows. Let \(f\) be an \(n\)-ary quadratic form over the integer ring of an algebraic number field \(F\), denote by \(h\) the number of classes in the genus of \(f\), and suppose that \(f\) is definite. Then \[ h\geq p([(n-5)/16]), \] where \(p\) is the partition function. This is proved by first showing (for either definite or indefinite \(f\)) that the genus contains a disjoint form if \(n\) is large enough.
Mathematics Subject Classification ID: 11E41
Mathematics Subject Classification ID: 11E04
zbMATH DE Number: 3422458
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3422458