Exterior power sums

Yanping Luo, Ruiyi Yang, Keheng Zhu

We prove that for every fixed $\hat{I}»>0$ and all sufficiently large $n$, any $z_1,\dots,z_n\in\C$ with $|z_j|\ge 1$ satisfy ${\max }_{2\le k\le n+1}|{\sum }_j{z}_j^k|>e^{-\hat{I}»n}$. Consequentl…