On a weak form of Ennola's conjecture about certain cubic number fields

TL;DR

This paper proves a weak version of Ennola's conjecture for certain cubic number fields by validating key assumptions related to Laurent polynomials using Newton identities.

Contribution

It confirms two main assumptions in Louboutin's work, advancing understanding of Ennola's conjecture in the context of cubic number fields.

Findings

Validated assumptions about Laurent polynomials over rationals

Established a weak form of Ennola's conjecture

Used Newton identities to prove key assumptions

Abstract

We establish a weak form of Ennola's conjecture. We achieve this by showing that two main assumptions Louboutin made in his previous work hold true. These assumptions are about Laurent polynomials over the rationals, and we prove them by using Newton identities.