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Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three

In: Mathematica Slovaca, vol. 66, no. 4
Jiří Klaška - Ladislav Skula

Details:

Year, pages: 2016, 1019 - 1027
Keywords:
cubic polynomial, type of factorization, discriminant
About article:
In this paper we extend our recent results concerning the validity of the law of inertia for the factorization of cubic polynomials over the Galois field $\Bbb{F}p$, $p$ being a prime. As the main result, the following theorem will be proved: Let $D\in \Bbb{Z}$ and let $CD$ be the set of all cubic polynomials $x3+ax2+bx+c\in\Bbb{Z}[x]$ with a discriminant equal to $D$. If $D$ is square-free and $3\nmid h(-3D)$ where $h(-3D)$ is the class number of $\Bbb{Q}(\sqrt{-3D})$, then all cubic polynomials in $CD$ have the same type of factorization over any Galois field $\Bbb{F}p$ where $p$ is a prime, $p>3$.
How to cite:
ISO 690:
Klaška, J., Skula, L. 2016. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three. In Mathematica Slovaca, vol. 66, no.4, pp. 1019-1027. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0199

APA:
Klaška, J., Skula, L. (2016). Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three. Mathematica Slovaca, 66(4), 1019-1027. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0199
About edition:
Published: 1. 8. 2016