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arXiv · 1910.06890

A characterization of polynomials whose high powers have non-negative coefficients

Marcus Michelen·Julian Sahasrabudhe
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Abstract

Let $f \in \mathbb{R}[x]$ be a polynomial with real coefficients. We say that $f$ is eventually non-negative if $f^m$ has non-negative coefficients for all sufficiently large $m \in \mathbb{N}$. In this short note, we give a classification of all eventually non-negative polynomials. This generalizes a theorem of De Angelis, and proves a conjecture of Bergweiler, Eremenko and Sokal

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Marcus Michelen, Julian Sahasrabudhe. 2020-12-31. A characterization of polynomials whose high powers have non-negative coefficients. https://arxiv.org/abs/1910.06890

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