Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three

Abstract

In this paper we extend our recent results concerning the validity of the law of inertia for the factorization of cubic polynomials over the Galois field

On cubic polynomials with a given discriminant

“…Creating tables of these representatives and analyzing them can lead to the discovery of new interesting facts. These tables can also be useful for a better understanding of the law of inertia for the factorization of cubic polynomials, which has been studied in [11][12][13][14][15][16].…”

“…Applying the method, the validity of Theorem 3.6 can be verified. 5,8,12,13,20,21,29,32,36,40,45,48,49,53,60,68,77,81,85,96,104,108,112,117,125,132,140,144,148,164,165,169,173,176,189,192,200,216,221,224,228,229,252,256,257,260,272,285,288,292,293,316,320,321,328,328,333,356,357,361,365,368,392,…”