Sign in
Back
On the number of non-real zeroes of a homogeneous differential polynomial and a generalisation of the Laguerre inequalities
Journal article   Peer reviewed

On the number of non-real zeroes of a homogeneous differential polynomial and a generalisation of the Laguerre inequalities

Mikhail Tyaglov and Mohamed J. Atia
Journal of mathematical analysis and applications, Vol.494(2), p.124652
15/02/2021
DOI: https://doi.org/10.1016/j.jmaa.2020.124652

Abstract

Laguerre inequalities Non-real zeroes Zeroes of polynomials
Given a real polynomial p with only real zeroes, we find upper and lower bounds for the number of non-real zeroes of the differential polynomialFϰ[p](z)=defp(z)p″(z)−ϰ[p′(z)]2, where ϰ is a real number. We also construct a counterexample to a conjecture by B. Shapiro [27] on the number of real zeroes of the polynomial Fn−1n[p](z) in the case when the real polynomial p of degree n has non-real zeroes. We formulate some new conjectures generalising the Hawaii conjecture.

Metrics

1 Record Views

Details