Publication details

Law of inertia for the factorization of cubic polynomials - the real case


SKULA Ladislav KLAŠKA Jiří

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

Faculty of Science

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. Assume that D<0, D is square-free and 3 does not divide the class number of Q((-3D)^(1/2)). We prove that all polynomials in C_D have the same type of factorization over any Galois field F_p, where p is a prime, p > 3.
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