Erdős problem 119

For unit-modulus complex numbers $z_i$ , let $p_n(z)=\prod_{i\le n}(z-z_i)$ and $M_n=\max_{|z|=1}|p_n(z)|$ . Erdős's prize question: is there $c>0$ with $\sum_{k\le n} M_k > n^{1+c}$ ?

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For unit-modulus complex numbers $z_i$, let $p_n(z)=\prod_{i\le n}(z-z_i)$ and $M_n=\max_{|z|=1}|p_n(z)|$. Erdős's prize question: is there $c>0$ with $\sum_{k\le n} M_k > n^{1+c}$?

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