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arXiv · 2103.07126

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

Myrial Ounaies·Georges Rhin·Jean Marc Sac-Épée
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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 $\{\vert x-1\vert<1\}$.

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Myrial Ounaies, Georges Rhin, Jean Marc Sac-Épée. 2021-03-12. On the relations between the zeros of a polynomial and its Mahler measure. https://doi.org/10.1016/j.jnt.2021.01.016

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