Publication detail

Quartic polynomials with a given discriminant

KLAŠKA, J.

Original Title

Quartic polynomials with a given discriminant

Type

journal article in Web of Science

Language

English

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.

Keywords

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

Authors

KLAŠKA, J.

Released

21. 2. 2022

Publisher

De Gruyter

Location

Slovakia

ISBN

1337-2211

Periodical

Mathematica Slovaca

Year of study

72

Number

1

State

Slovak Republic

Pages from

35

Pages to

50

Pages count

16

URL

https://www.degruyter.com/document/doi/10.1515/ms-2022-0003/html

Full text in the Digital Library

http://hdl.handle.net/11012/203964

BibTex

@article{BUT176796,
  author="Jiří {Klaška}",
  title="Quartic polynomials with a given discriminant",
  journal="Mathematica Slovaca",
  year="2022",
  volume="72",
  number="1",
  pages="35--50",
  doi="10.1515/ms-2022-0003",
  issn="1337-2211",
  url="https://www.degruyter.com/document/doi/10.1515/ms-2022-0003/html"
}