Detail publikace

Quartic polynomials with a given discriminant

KLAŠKA, J.

Originální název

Quartic polynomials with a given discriminant

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

KLAŠKA, J.

Vydáno

21. 2. 2022

Nakladatel

De Gruyter

Místo

Slovakia

ISSN

1337-2211

Periodikum

Mathematica Slovaca

Ročník

72

Číslo

1

Stát

Slovenská republika

Strany od

35

Strany do

50

Strany počet

16

URL

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

Plný text v Digitální knihovně

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"
}