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

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...

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Bibliographic Details
Published in:Journal of number theory 2021-07, Vol.224, p.165-190
Main Authors: Ounaies, M., Rhin, G., Sac-Épée, J.-M.
Format: Article
Language:English
Subjects:
Integer polynomials
Mahler measure
Mathematics
Number Theory
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Summary: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|
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2021.01.016