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KLAŠKA, J. SKULA, L.
Original Title
Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
Cubic polynomial, type of factorization, discriminant
Authors
KLAŠKA, J.; SKULA, L.
Released
15. 3. 2017
Publisher
De Gruyter
Location
Slovakia
ISBN
0139-9918
Periodical
Mathematica Slovaca
Year of study
67
Number
1
State
Slovak Republic
Pages from
71
Pages to
82
Pages count
12
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", journal="Mathematica Slovaca", year="2017", volume="67", number="1", pages="71--82", doi="10.1515/ms-2016-0248", issn="0139-9918" }