Publication detail

LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE

KLAŠKA, J. SKULA, L.

Original Title

LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE

English Title

LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE

Type

journal article in Web of Science

Language

en

Original Abstract

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, $p > 3$.

English abstract

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, $p > 3$.

Keywords

cubic polynomial, type of factorization, discriminant

Released

07.04.2017

Publisher

Utilitas Mathematica Publishing

Location

Kanada

Pages from

39

Pages to

50

Pages count

12

Documents

BibTex


@article{BUT134731,
  author="Jiří {Klaška}",
  title="LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE",
  annote="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, $p > 3$.",
  address="Utilitas Mathematica Publishing",
  chapter="134731",
  howpublished="print",
  institution="Utilitas Mathematica Publishing",
  number="1",
  volume="102",
  year="2017",
  month="april",
  pages="39--50",
  publisher="Utilitas Mathematica Publishing",
  type="journal article in Web of Science"
}