关于复数和的模与模的和之比的一个极值问题

An Extreme Value Problem on Ratios of Norms of Sums to Sums of Norms of Complex Numbers

本文考虑了m个复数的部分和的模的最大值与全体复数模的和之比的下确界ξm。通过引进复数集的对称分解及O-重心集等概念,当m=λ·2~μ不是2的整数方幂时,或当m=2,4时,我们求出了ξm的准确值;当m=2~μ是2的整数方幂(μ≥3)时,我们亦得到了ξm的大小的较为精确的估计式。

In this paper, the greatest lower bound V is a set of m complex numbers which are not all zero was considered. We found the exact value of ξ_m for m =λ·2~μ and m=2,4, and obtained an inequality that gives a more accurate estimation of the value of ξ_m for m=2~μ (μ≥3).