论文标题
从渐近形成到Keiper/Li方法的封闭形式到Riemann假设
From asymptotic to closed forms for the Keiper/Li approach to the Riemann Hypothesis
论文作者
论文摘要
Riemann假设（RH） - Riemann Zeta函数的所有非真实零零应具有实际的1/2-仍然是一个主要的开放问题。它最具体的等效物是无限数字keiper--li常数的无限序列应无处不在（Li的标准）。但是这些数字在分析上难以捉摸且难以计算，因此我们寻求更简单的变体。对该序列RH的基本敏感性在于其渐近尾巴。然后，保留此功能，我们可以修改keiper-li方案，以获得基本封闭形式的新序列。这可以进行更明确的分析，并进行更轻松，更快的计算。此外，我们可以通过观察Davenport的类似物（Heilbronn反例）向RH进行观察，即可表明新序列将如何通过观察其对Davenport的类似物来向Rh-Violation Zeros发出信号。
The Riemann Hypothesis (RH) - that all nonreal zeros of Riemann's zeta function shall have real part 1/2 - remains a major open problem. Its most concrete equivalent is that an infinite sequence of real numbers, the Keiper--Li constants, shall be everywhere positive (Li's criterion). But those numbers are analytically elusive and strenuous to compute, hence we seek simpler variants. The essential sensitivity to RH of that sequence lies in its asymptotic tail; then, retaining this feature, we can modify the Keiper--Li scheme to obtain a new sequence in elementary closed form. This makes for a more explicit analysis, with easier and faster computations. We can moreover show how the new sequence will signal RH-violating zeros if any, by observing its analogs for the Davenport--Heilbronn counterexamples to RH.
