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

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 } .