User:Blankuser/Cohn Schur Criterion

The quadratic equation formed from $\rho (w)-z\sigma (w)$ and rearranged:

$aw^{2}+bw+c,~~a,b,c\in \mathbb {C}$

obeys the root condition if and only if:

$\left|a\right|^{2}-\left|c\right|^{2}\geq 0$

$\left(\left|a\right|^{2}-\left|c\right|^{2}\right)^{2}\geq \left|a{\bar {b}}-b{\bar {c}}\right|^{2}$

and if the latter is obeyed as an equality then:

$\left|b\right|<2\left|a\right|$

.