Detail publikace

Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3

Originální název

Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3

Anglický název

Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3

Jazyk

en

Originální abstrakt

Let $D \in \mathbb Z$ and let $C_D$ be the set of all monic cubic polynomials $x^3+ax^2+bx+c\in \mathbb Z[x]$ with the discriminant equal to $D$. Along the line of our preceding papers, the following Theorem has been proved: If $D$ is square-free and $3 \nmit h(-3D)$ where $h(-3D)$ is the class number of $\mathbbQ( \sqrt(-3D)$, then all polynomials in $C_D$ have the same type of factorization over the Galois field $F_p$ where $p$ is a prime, $p > 3$. In this paper, we prove the validity of the above implication also for primes 2 and 3.

Anglický abstrakt

Let $D \in \mathbb Z$ and let $C_D$ be the set of all monic cubic polynomials $x^3+ax^2+bx+c\in \mathbb Z[x]$ with the discriminant equal to $D$. Along the line of our preceding papers, the following Theorem has been proved: If $D$ is square-free and $3 \nmit h(-3D)$ where $h(-3D)$ is the class number of $\mathbbQ( \sqrt(-3D)$, then all polynomials in $C_D$ have the same type of factorization over the Galois field $F_p$ where $p$ is a prime, $p > 3$. In this paper, we prove the validity of the above implication also for primes 2 and 3.

BibTex


@article{BUT134703,
  author="Jiří {Klaška} and Ladislav {Skula}",
  title="Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3",
  annote="Let $D \in \mathbb Z$ and let $C_D$  be the set of all monic cubic polynomials $x^3+ax^2+bx+c\in \mathbb Z[x]$ with the discriminant equal to $D$. Along the line of our preceding papers, the following Theorem has
been proved: If $D$ is square-free and $3 \nmit h(-3D)$ where $h(-3D)$ is the class number of $\mathbbQ(
\sqrt(-3D)$, then all polynomials in $C_D$ have the same type of factorization over the Galois field $F_p$ where $p$ is a prime,
$p > 3$. In this paper, we prove the validity of the above implication also for primes 2 and 3.",
  address="De Gruyter",
  chapter="134703",
  doi="10.1515/ms-2016-0248",
  howpublished="print",
  institution="De Gruyter",
  number="1",
  volume="67",
  year="2017",
  month="march",
  pages="71--82",
  publisher="De Gruyter",
  type="journal article in Web of Science"
}