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@article{1376985,
author = {Klaška, Jiří and Skula, Ladislav},
article_location = {BERLIN},
article_number = {1},
doi = {http://dx.doi.org/10.1515/ms-2016-0248},
keywords = {cubic polynomial; type of factorization; discriminant},
language = {eng},
issn = {0139-9918},
journal = {Mathematica Slovaca},
title = {Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3},
url = {https://www.degruyter.com/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml},
volume = {67},
year = {2017}
}
TY - JOUR
ID - 1376985
AU - Klaška, Jiří - Skula, Ladislav
PY - 2017
TI - Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3
JF - Mathematica Slovaca
VL - 67
IS - 1
SP - 71-82
EP - 71-82
PB - WALTER DE GRUYTER GMBH
SN - 01399918
KW - cubic polynomial
KW - type of factorization
KW - discriminant
UR - https://www.degruyter.com/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml
L2 - https://www.degruyter.com/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml
N2 - Let D be an integer and let C_D be the set of all monic cubic polynomials x^3 + ax^2 + bx + c with integral coefficients and 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 does not divide the class number of Q((-3D)^(1/2)), 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.
ER -
KLAŠKA, Jiří and Ladislav SKULA. Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3. \textit{Mathematica Slovaca}. BERLIN: WALTER DE GRUYTER GMBH, 2017, vol.~67, No~1, p.~71-82. ISSN~0139-9918. Available from: https://dx.doi.org/10.1515/ms-2016-0248.
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