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One-class genera of positive ternary quadratic forms

Published online by Cambridge University Press:  26 February 2010

G. L. Watson
G. L. Watson
Affiliation:
University College, London.
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Extract

We consider positive-definite ternary quadratic forms with integer coefficients. Such a form, f, can be written in matrix notation as

Here x′ is the transpose of the column vector x = {x1, x2, x3) and a,ij = aji is the coefficient of xixj in f. Clearly det A is positive and even and so

is a negative integer.

Type
Research Article
Information
Mathematika , Volume 19 , Issue 1 , June 1972 , pp. 96 - 104
Copyright
Copyright © University College London 1972

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References

1.Watson, G. L., Integral quadratic forms (Cambridge Tract No. 51 (Cambridge, 1960).Google Scholar
2.Watson, G. L., “Transformations of a quadratic form which do not increase the class-number”, Proc. London Math. Soc. (3), 12 (1962), 577–587.CrossRefGoogle Scholar
3.Watson, G. L., “The class-number of a positive quadratic form”, Proc. London Math. Soc. (3), 13 (1963), 549–576.CrossRefGoogle Scholar
4.Pall, Gordon and Burton, W. Jones, “Regular and semi-regular positive ternary quadratic forms”, Acta Mathematica, 70 (1939), 165–191.Google Scholar