Some properties of the quadrinomials $p(z)=1+\kappa (z+z^{N-1})+z^N$ and $q(z)=1+\kappa (z-z^{N-1})-z^N$

Dmitriy Dmitrishin, Alexander Stokolos

We show that all the zeros of the quadrinomial $p(z)=1+\kappa (z+z^{N-1})+z^N$ lie on the unit circle if and only if the inequalities \[ -1\leκ\le 1\; (\mbox{ if $N$ is even}),\;\; -1\le…