Almost regular quaternary quadratic forms
Annales de l'Institut Fourier, Volume 58 (2008) no. 5, p. 1499-1549
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 p37. 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.
Nous étudions les formes quadratiques entières quaternaires (c’est-à-dire à quatre variables) qui sont définies positives et presque régulières. Nous montrons en particulier qu’une telle forme n’est p-anisotrope que pour au plus un nombre premier p. De plus, pour un nombre premier p, il existe une forme quadratique quaternaire presque régulière p-anisotrope si et seulement si p37. Nous étudions également les genres contenant une forme quadratique presque régulière p-anisotrope. Nous démontrons plusieurs résultats de finitude concernant les familles de ces genres et établissons des critères effectifs presque réguliers.
DOI : https://doi.org/10.5802/aif.2391
Classification:  11E12,  11E20
Keywords: Quadratic equations, almost regular quadratic forms
@article{AIF_2008__58_5_1499_0,
     author = {Bochnak, Jacek and Oh, Byeong-Kweon},
     title = {Almost regular quaternary quadratic forms},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {5},
     year = {2008},
     pages = {1499-1549},
     doi = {10.5802/aif.2391},
     zbl = {1162.11020},
     mrnumber = {2445826},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2008__58_5_1499_0}
}
Bochnak, Jacek; Oh, Byeong-Kweon. Almost regular quaternary quadratic forms. Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1499-1549. doi : 10.5802/aif.2391. https://aif.centre-mersenne.org/item/AIF_2008__58_5_1499_0/

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