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A second genus of regular ternary forms. (English) Zbl 0841.11017

It is proved that the ternary quadratic forms \(f= x^2+ y^2+ 7z^2+ yz\) and \(g= x^2+ 2y^2+ 4z^2+ xy+ yz\), which constitute a genus with discriminant 27, are both regular. Without proof it is reported that \(x^2+ 4y^2+ 7z^2+ xz\) and \(x^2+ 5y^2+ 7z^2+ xy+ 5yz\) (constituting a genus of discriminant 108) are also both regular. The same phenomenon was observed earlier for two other forms of discriminant 27 by J. S. Hsia.

MSC:

11E20 General ternary and quaternary quadratic forms; forms of more than two variables
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References:

[1] Hsia, Mathematika 28 pp 231– (1981)
[2] Brandt, Abh. S chs. Akad. Wiss. Math. Nat. Kl. 45 (1958)
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