User:Blankuser/Cohn Schur Criterion

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< User:Blankuser

The quadratic equation formed from $ρ(w) - z σ(w)$ and rearranged:

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

obeys the root condition if and only if:

$\left|a\right|^2-\left|c\right|^2\ge 0$

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

and if the latter is obeyed as an equality then:

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

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