Experimental Mathematics

Equality of Polynomial and Field Discriminants

Avner Ash, Jos Brakenhoff, and Theodore Zarrabi

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Abstract

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.

Article information

Source
Experiment. Math., Volume 16, Issue 3 (2007), 367-374.

Dates
First available in Project Euclid: 7 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.em/1204928536

Mathematical Reviews number (MathSciNet)
MR2367325

Zentralblatt MATH identifier
1166.11035

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11C08: Polynomials [See also 13F20]

Keywords
Discriminant polynomial number field monogenic square-free Dedekind's criterion

Citation

Ash, Avner; Brakenhoff, Jos; Zarrabi, Theodore. Equality of Polynomial and Field Discriminants. Experiment. Math. 16 (2007), no. 3, 367--374. https://projecteuclid.org/euclid.em/1204928536


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