Publication details

Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3

Authors

KLAŠKA Jiří SKULA Ladislav

Year of publication 2017
Type Article in Periodical
Magazine / Source Mathematica Slovaca
MU Faculty or unit

Faculty of Science

Citation
Web https://www.degruyter.com/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml
Doi http://dx.doi.org/10.1515/ms-2016-0248
Field General mathematics
Keywords cubic polynomial; type of factorization; discriminant
Description 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.
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