Geodesic
On the roots of polynomials with log-convex coefficients
Canadian journal of mathematics, Tome 75 (2023) no. 2, pp. 470-493

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DOI

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.
DOI : 10.4153/S0008414X22000062
Mots-clés : Dual Steiner polynomials, dual quermassintegrals, log-convex sequences, log-convex coefficients polynomials, properties of roots 
Cifre, María A. Hernández; Tárraga, Miriam; Nicolás, Jesús Yepes. On the roots of polynomials with log-convex coefficients. Canadian journal of mathematics, Tome 75 (2023) no. 2, pp. 470-493. doi: 10.4153/S0008414X22000062
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     title = {On the roots of polynomials with log-convex coefficients},
     journal = {Canadian journal of mathematics},
     pages = {470--493},
     year = {2023},
     volume = {75},
     number = {2},
     doi = {10.4153/S0008414X22000062},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000062/}
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