# Almost regular quaternary quadratic forms

Jacek Bochnak^{[1]}; Byeong-Kweon Oh^{[2]}

- [1] Vrije Universiteit Department of Mathematics 1081 HV Amsterdam De Boelelaan 1081 A (The Netherlands)
- [2] Sejong University Department of Applied Mathematics Seoul, 143-747 (Korea)

Annales de l’institut Fourier (2008)

- Volume: 58, Issue: 5, page 1499-1549
- ISSN: 0373-0956

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topBochnak, Jacek, and Oh, Byeong-Kweon. "Almost regular quaternary quadratic forms." Annales de l’institut Fourier 58.5 (2008): 1499-1549. <http://eudml.org/doc/10355>.

@article{Bochnak2008,

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.},

affiliation = {Vrije Universiteit Department of Mathematics 1081 HV Amsterdam De Boelelaan 1081 A (The Netherlands); Sejong University Department of Applied Mathematics Seoul, 143-747 (Korea)},

author = {Bochnak, Jacek, Oh, Byeong-Kweon},

journal = {Annales de l’institut Fourier},

keywords = {Quadratic equations; almost regular quadratic forms; quadratic equations},

language = {eng},

number = {5},

pages = {1499-1549},

publisher = {Association des Annales de l’institut Fourier},

title = {Almost regular quaternary quadratic forms},

url = {http://eudml.org/doc/10355},

volume = {58},

year = {2008},

}

TY - JOUR

AU - Bochnak, Jacek

AU - Oh, Byeong-Kweon

TI - Almost regular quaternary quadratic forms

JO - Annales de l’institut Fourier

PY - 2008

PB - Association des Annales de l’institut Fourier

VL - 58

IS - 5

SP - 1499

EP - 1549

AB - 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.

LA - eng

KW - Quadratic equations; almost regular quadratic forms; quadratic equations

UR - http://eudml.org/doc/10355

ER -

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