Polynomials with all zeros on the unit circle (Q624246)

A univariate polynomial \(p(z)=\sum_{k=0}^m A_k z^k \in {\mathbb C}[z]\) is called self-inversive if there exists \(\theta \in {\mathbb R}\) such that \(A_{m-k} = e^{i\theta} \bar{A}_k\) for all \(k\). The authors give a sufficient condition for all the zeros of a self-inversive polynomial to lie on the unit circle. The condition is piecewise-linear and depends on three complex parameters to be found.