论文标题
关于Riemann Zeta Zeros的自我复制特性：一项统计研究
On the self-replicating properties of Riemann zeta zeros: A statistical study
论文作者
论文摘要
我们在大距离上研究了未量化的Riemann Zeta Zeros的差异分布，$γ-γ^{'} $。我们证明，与高度无关，连续数量的一部分零数知道较低层的位置。零子集中包含的信息与$ ln（γ/（2π））$成反比，其中$γ$是子集的平均zeta。因为零的平均差异也与$ ln（γ/（2π））$成反比，所以线$ \ re（z）= 1/2 $的每个段都包含相等的信息。差异的分布偏向最接近的Zeta Zero，或者至少在附近的零零的情况下，当Zeta Zero沿增加方向越过时，偏度总是会降低。我们还表明，分布的方差具有局部最大值，或者至少在每个Zeta Zero处有一个转折点，即方差的第二个导数的局部最小值。此外，似乎零越高，差异的分布越多地位于偏度 - 毛细生植物平面中。约翰逊分布的灵活性使我们能够很好地拟合分布，尽管偏度和分布的峰度值。
We study distributions of differences of unscaled Riemann zeta zeros, $γ-γ^{'}$, at large distances. We show, that independently of the height, a subset of finite number of successive zeros knows the locations of lower level zeros. The information contained in the subset of zeros is inversely proportional to $ln(γ/(2π))$, where $γ$ is the average zeta of the subset. Because the mean difference of the zeros also decreases as inversely proportional to $ln(γ/(2π))$, each equally long segment of the line $\Re(z)=1/2$ contains equal amount of information. The distributions of differences are skewed towards the nearest zeta zero, or at least, in the case of very nearby zeros, the skewness always decreases when zeta zero is crossed in increasing direction. We also show that the variance of distributions has local maximum or, at least, a turning point at every zeta zero, i.e., local minimum of the second derivative of the variance. In addition, it seems that the higher the zeros the more compactly the distributions of the differences are located in the skewness-kurtosis -plane. The flexibility of the Johnson distribution allows us to fit the distributions nicely, despite of the values of skewness and kurtosis of the distributions.
