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Almost regular quaternary quadratic forms

Jacek BochnakByeong-Kweon Oh — 2008

Annales de l’institut Fourier

We investigate the almost regular positive definite integral quaternary quadratic forms. In particular, we show that every such form is p -anisotropic for at most one prime number p . Moreover, for a prime p there is an almost regular p -anisotropic quaternary quadratic form if and only if p 37 . We also study the genera containing some almost regular p -anisotropic quaternary form. We show several finiteness results concerning the families of these genera and give effective criteria for almost regularity....

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