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Classification of one-class spinor genera for quaternary quadratic forms. (English) Zbl 1456.11040

The authors prove the following theorem: Let \(f\) be a primitive integral positive definite quaternary quadratic form for which the spinor genus and class coincide. Then either the genus and class of \(f\) coincide or \(f\) is equivalent to the form \[x^2+ xy+ 7y^2+ 3z^2+ 3zw+ 3w^2\] of discriminant \(3^6= 729\).

MSC:

11E20 General ternary and quaternary quadratic forms; forms of more than two variables
11E12 Quadratic forms over global rings and fields

Software:

LMFDB; Magma; SageMath
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References:

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