Detail publikace
LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE
KLAŠKA, J. SKULA, L.
Anglický název
LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
Let $D\in Z$ and $C_D := \{f(x) = x^3 + ax^2 + b^x + c\in Z[x];D_f = D\}$ where $D_f$ is the discriminant of $f(x)$. Assume that $D < 0$, $D$ is square-free, $3\nmid D$, and $3 \nmid h(-3D)$ where $h(-3D)$ is the class number of $Q(\sqrt -3D)$. We prove that all polynomials in $C_D$ have the same type of factorization over any Galois field $ F_p$, $p$ being a prime, $p > 3$.
Anglický abstrakt
Let $D\in Z$ and $C_D := \{f(x) = x^3 + ax^2 + b^x + c\in Z[x];D_f = D\}$ where $D_f$ is the discriminant of $f(x)$. Assume that $D < 0$, $D$ is square-free, $3\nmid D$, and $3 \nmid h(-3D)$ where $h(-3D)$ is the class number of $Q(\sqrt -3D)$. We prove that all polynomials in $C_D$ have the same type of factorization over any Galois field $ F_p$, $p$ being a prime, $p > 3$.
Klíčová slova anglicky
cubic polynomial, type of factorization, discriminant
Vydáno
07.04.2017
Nakladatel
Utilitas Mathematica Publishing
Místo
Kanada
ISSN
0315-3681
Ročník
102
Číslo
1
Strany od–do
39–50
Počet stran
12
BIBTEX
@article{BUT134731,
author="Jiří {Klaška},
title="LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE",
year="2017",
volume="102",
number="1",
month="April",
pages="39--50",
publisher="Utilitas Mathematica Publishing",
address="Kanada",
issn="0315-3681"
}