关于正数的幂和
On Power Sums of Positive Numbers
摘要：
本文利用Hausdorff矩问题和Mergelyan定理建立了亏格$0$整函数$f(z)$仅有正零点的充要条件，所得判据与李先金关于黎曼假设的判据非常相似.我们也将这一准则应用于黎曼假设和广义黎曼假设的某些Dirichlet $L$ -系列的真正的原始字符。
英文摘要：
In this work we establish a necessary and sufficient condition for a genus $0$ entire function $f(z)$ has only positive zeros by applying Hausdorff moment problem and Mergelyan's theorem, the obtained criterion is very much reminiscent of Xian-Jin Li's criterion on the Riemann hypothesis. We also apply this criterion to the Riemann hypothesis and the generalized Riemann hypothesis for certain Dirichlet $L$-series of real primitive characters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
