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

TL;DR

This paper explores the relationship between polynomial zeros and Mahler measure, providing bounds on real zeros, distances from zeros to the unit circle, and zeros within a specific disk.

Contribution

It introduces new estimates and bounds connecting polynomial zeros with Mahler measure, advancing understanding of their interrelations.

Findings

Bounds on the number of real zeros

Lower bounds on distances from zeros to the unit circle

Lower bounds on zeros within a specific disk

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 $\{\vert x-1\vert<1\}$.