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KLAŠKA, J. SKULA, L.
Original Title
LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE
Type
journal article in Web of Science
Language
English
Original Abstract
Let $D\in Z$ and $C_D := \{f(x) = x^3 + ax^2 + b^x + c\in Z[x];D_f = D\}$ where $D_f$ is the discriminant of $f(x)$. Assume that $D < 0$, $D$ is square-free, $3\nmid D$, and $3 \nmid h(-3D)$ where $h(-3D)$ is the class number of $Q(\sqrt -3D)$. We prove that all polynomials in $C_D$ have the same type of factorization over any Galois field $ F_p$, $p$ being a prime, $p > 3$.
Keywords
cubic polynomial, type of factorization, discriminant
Authors
Released
7. 4. 2017
Publisher
Utilitas Mathematica Publishing
Location
Kanada
ISBN
0315-3681
Periodical
UTILITAS MATHEMATICA
Year of study
102
Number
1
State
Canada
Pages from
39
Pages to
50
Pages count
12
BibTex
@article{BUT134731, author="Jiří {Klaška}", title="LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE", journal="UTILITAS MATHEMATICA", year="2017", volume="102", number="1", pages="39--50", issn="0315-3681" }