论文标题
Keiper-LI系数的分析扩展
Analytic Extension of Keiper-Li Coefficients
论文作者
论文摘要
我们构建了某些整个函数$λ$，对于整数s $，它与众所周知的keiper-li系数相吻合，即$λ（n）=λ_{n} $。这是一个均匀的函数$λ（s）=λ（-s）$，并且具有表现出有趣分布的复杂零的无限。包括3500多个复杂零的$λ（s）$，精度为14个重要位数的表。对这些零的分布的详细分析可能会揭示Riemann假设。事实证明，可能违反黎曼假说（如果是这种情况）会明确反映在这些零的特定分布中。更具体地说，如果Riemann假设为真，则它们会形成复杂的四弦，如果它是错误的，则将真实的双线对齐。
We construct certain entire function $λ(s)$ which for integer s coincides with the well-known Keiper-Li coefficients, i.e. $λ(n)=λ_{n}$. This is an even function $λ(s)=λ(-s)$ and has an infinitude of complex zeros exhibiting interesting distribution. Extensive tables of more than 3500 complex zeros of $λ(s)$ with precision of 14 significant digits are included. A detailed analysis of the distribution of these zeros may shed some light on the Riemann hypothesis. It turns out that possible violation of the Riemann hypothesis (if such is the case) would be clearly reflected in the specific distribution of these zeros. More specifically, they form complex quadruplets if the Riemann hypothesis is true, and aligned real doublets if it is false.
