Let $p (z) = \prod_{i = 1}^{n} (z - z_{i})$ for $∣ z_{i} ∣ \leq 1$ . Is it true that $∣{z : ∣ p (z)∣ < 1}∣ > n^{- O (1)}$ (or perhaps even $> (lo g n)^{- O (1)}$ )?

Worked, still open.

polynomials · solved · 0 attempts

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