Une nouvelle minoration pour la trace des entiers alg\'ebriques totalement positifs

TL;DR

This paper introduces a refined recursive algorithm that improves lower bounds for the absolute trace of totally positive algebraic integers and explores their relationship with reciprocal integers.

Contribution

It presents a novel variant of an existing recursive algorithm to enhance bounds on algebraic integer traces and connects these traces with reciprocal algebraic integers.

Findings

Improved lower bounds for the absolute trace of totally positive algebraic integers.

Established a link between the traces of totally positive algebraic integers and their reciprocals.

Demonstrated the effectiveness of the modified recursive algorithm.

Abstract

We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic integer and the absolute trace of a totally positive reciprocal integer.