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"
}