Generalizations of Goncalves' inequality

Peter Borwein, Michael J. Mossinghoff, Jeffrey D. Vaaler

If $F$ is a polynomial with complex coefficients, leading term $a_N$, and roots ${\alpha }_1$, ..., ${\alpha }_N$, then Gonçalves' inequality states that $\Vert F{\Vert }_2^2$ is bounded below by $\abs{a_N}…