2026/07/24 by Yanping Luo, Ruiyi Yang, Keheng Zhu
#math.CO #math.NT
We prove that for every fixed λ>0 and all sufficiently large n, any z1,…,zn∈\C with |zj|≥1 satisfy max2≤ k≤ n+1|∑j zjk|>e-λn. Consequently, the nth root of the optimal maximum tends to 1, so no constant C>1 in Erdős 973 can exist. The proof combines a truncated exponential factorization with overconvergence on an open set outside the unit disk and a normal-family obstruction for Cauchy transforms.