Publication detail

Quartic polynomials with a given discriminant

KLAŠKA, J.

English title

Quartic polynomials with a given discriminant

Type

journal article in Web of Science

Language

en

Original abstract

Let $ 0\ne D \in \Bbb Z$ and let $Q_D$ be the set of all monic quartic polynomials $ x^4 +ax^3 +bx^2 + cx + d \in \Bbb Z[x]$ with the discriminant equal to $D$. In this paper we will devise a method for determining the set $Q_D$. Our method is strongly related to the theory of integral points on elliptic curves. The well-known Mordell's equation plays an important role as well in our considerations. Finally, some new conjectures will be included inspired by extensive calculation on a computer.

English abstract

Let $ 0\ne D \in \Bbb Z$ and let $Q_D$ be the set of all monic quartic polynomials $ x^4 +ax^3 +bx^2 + cx + d \in \Bbb Z[x]$ with the discriminant equal to $D$. In this paper we will devise a method for determining the set $Q_D$. Our method is strongly related to the theory of integral points on elliptic curves. The well-known Mordell's equation plays an important role as well in our considerations. Finally, some new conjectures will be included inspired by extensive calculation on a computer.

Keywords in English

quartic polynomial, discriminant, Mordell's equation, elliptic curve

Released

21.02.2022

Publisher

De Gruyter

Location

Slovakia

ISSN

1337-2211

Volume

72

Number

1

Pages from–to

35–50

Pages count

16

BIBTEX


@article{BUT176796,
  author="Jiří {Klaška},
  title="Quartic polynomials with a given discriminant",
  year="2022",
  volume="72",
  number="1",
  month="February",
  pages="35--50",
  publisher="De Gruyter",
  address="Slovakia",
  issn="1337-2211"
}