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Jacek Bochnak; Byeong-Kweon Oh
Almost regular quaternary quadratic forms
(Formes quadratiques quaternaires presque régulières)
Annales de l'institut Fourier, 58 no. 5 (2008), p. 1499-1549, doi: 10.5802/aif.2391
Article PDF | Reviews MR 2445826 | Zbl 1162.11020
Class. Math.: 11E12, 11E20
Keywords: Quadratic equations, almost regular quadratic forms

Résumé - Abstract

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 $p \le 37$. 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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