Spinor genera of binary quadratic forms
type: Item
instance of: scholarly article
title: Spinor genera of binary quadratic forms
zbMATH Open document ID: 0268.10010
DOI: 10.1016/0022-314X(73)90012-7
author: Dennis R. Estes
author: Gordon Pall
published in: Journal of Number Theory
publication date: 1973-01-01T00:00:00Z
review text: The authors show how the modern theory of spinor genera, of binary quadratic forms, can be made to fit in with the Gaussian theory of genera. Using the letters \(f,g,h,k\) to denote forms with integer coefficients and fixed non-zero discriminant \(d\), let \(gh\) denote the Gaussian composition of \(g\) and \(h\). Then the authors show that \(f\) and \(g\) are in the same spinor genus if and only if \(f = gk^4\) for some \(k\); the corresponding Gaussian result being that \(f,g\) are in the same genus if and only if \(f = gh^2\) for some \(h\). They construct spinor generic characters, and investigate in detail some cases in which the discriminant \(d\) has a simple arithmetical structure.
Mathematics Subject Classification ID: 11E16
zbMATH DE Number: 3422459
zbMATH Keywords: spinor genera
zbMATH Keywords: binary quadratic forms
zbMATH Keywords: Gaussian theory of genera
zbMATH Keywords: Gaussian composition
MaRDI profile type: Publication
cites work: Q3262865
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description: scientific article; zbMATH DE number 3422459