On the relations between the zeros of a polynomial and its Mahler measure

Myrial Ounaies; Georges Rhin; Jean Marc Sac-Épée

doi:10.1016/j.jnt.2021.01.016

paper

On the relations between the zeros of a polynomial and its Mahler measure

arXiv:2103.07126 · doi:10.1016/j.jnt.2021.01.016

Abstract

In this work, we are dealing with some properties relating the zeros of a polynomial and its Mahler measure. We provide estimates on the number of real zeros of a polynomial, lower bounds on the distance between the zeros of a polynomial and non-zeros located on the unit circle and a lower bound on the number of zeros of a polynomial in the disk ${∣ x - 1∣ < 1}$ .