Cubic polynomials defining monogenic fields with the same discriminant

Abstract

Let K be a number field with ring of integers OK . K is said to be monogenic if OK = Z[θ] for some θ ∈ OK . Monogeneity of a number field is not always guaranteed. Furthermore, it is rare for two number fields to have the same discriminant, thus finding fields with these two properties is an interesting problem. In this paper we show that there exist infinitely many triples of polynomials defining distinct monogenic cubic fields with the same discriminant.