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The positive values of inhomogeneous ternary quadratic forms

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes
E. S. Barnes
Affiliation:
University of Adelaide.
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Let f(x, y, z) be an indefinite ternary quadratic form of signature (2, 1) and determinant d ≠ 0. Davenport [3] has shown that there exist integral x, y, z with, the equality sign being necessary if and only if f is a positive multiple of f1(x, y, z) = x2 + yz.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 2 , October 1961 , pp. 127 - 132
Copyright
Copyright © Australian Mathematical Society 1961

References

[1]Barnes, E. S. and Swinnerton-Dyer, H. P. F.The inhomogeneous minima of binary quadratic forms (III), Acta Math. 92 (1954), 199–234.CrossRefGoogle Scholar
[2]Blaney, H.Some asymmetric inequalities, Proc. Cambridge Phil. Soc. 46 (1950), 359–376.CrossRefGoogle Scholar
[3]Davenport, H.On indefinite ternary quadratic forms, Proc. London Math. Soc. (2) 51 (1949), 145–160.CrossRefGoogle Scholar