Erdős problem 1039 · problems.science

For $f(z) = \prod_{i=1}^n (z - z_i)$ with all $|z_i| \le 1$ , let $\rho(f)$ be the radius of the largest disc contained in $\{z : |f(z)| < 1\}$ . Is $\rho(f) \gg 1/n$ ? The worst case is now known to be $\Theta(1/n)$ , with the explicit bound $\rho(f) \ge (\log 2)/n$ .

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