We give a conjecture concerning when the discriminant of an irreducible monic integral polynomial equals the discriminant of the field defined by adjoining one of its roots to $ \Q$. We discuss computational evidence for it. An appendix by the second author gives a conjecture concerning when the discriminant of an irreducible monic integral polynomial is square-free and some computational evidence for it.
Publié le : 2007-05-15
Classification:
Discriminant,
polynomial,
number field,
monogenic,
square-free,
Dedekind's criterion,
11R29,
11C08
@article{1204928536,
author = {Ash, Avner and Brakenhoff, Jos and Zarrabi, Theodore},
title = {Equality of Polynomial and Field Discriminants},
journal = {Experiment. Math.},
volume = {16},
number = {1},
year = {2007},
pages = { 367-374},
language = {en},
url = {http://dml.mathdoc.fr/item/1204928536}
}
Ash, Avner; Brakenhoff, Jos; Zarrabi, Theodore. Equality of Polynomial and Field Discriminants. Experiment. Math., Tome 16 (2007) no. 1, pp. 367-374. http://gdmltest.u-ga.fr/item/1204928536/