M. A. Hernández Cifre, Miriam Tárraga, J. Yepes Nicolás
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On the roots of polynomials with log-convex coefficients
Abstract In this paper, we consider the family of nth degree polynomials whose coefficients form a log-convex sequence (up to binomial weights), and investigate their roots. We study, among others, the structure of the set of roots of such polynomials, showing that it is a closed convex cone in the upper half-plane, which covers its interior when n tends to infinity, and giving its precise description for every
$n\in \mathbb {N}$
,
$n\geq 2$
. Dual Steiner polynomials of star bodies are a particular case of them, and so we derive, as a consequence, further properties for their roots.