论文标题
关于Zeta Zeros差异的统计数据，从零数字$ 10^{23} $
On the statistics of differences of zeta zeros starting from zero number $10^{23}$
论文作者
论文摘要
我们研究了未量化的Riemann Zeta Zeros的差异分布，$γ-γ^{'} $，整个。我们表明，独立于零的位置，即，即使对于零高达$ 10^{23} $的零，它们的差异也具有相似的统计属性。差异的分布通常偏向最接近的Zeta零。但是，我们表明并非总是如此，而是取决于相应分布每一侧附近零的距离和数量。然而，当从左到右（即沿增加方向）交叉时，偏度始终会减小。此外，我们表明，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。此外，我们表明，尽管分布的偏度或峰度的价值，但分布仍可以拟合约翰逊概率密度函数。
We study distributions of differences of unscaled Riemann zeta zeros, $γ-γ^{'}$, at large. We show, that independently of the location of the zeros, i.e., even for zeros as high as $10^{23}$, their differences have similar statistical properties. The distributions of differences are skewed usually towards the nearest zeta zero. We show, however, that this is not always the case, but depends upon the distance and number of nearby zeros on each side of the corresponding distribution. The skewness, however, always decreases when zeta zero is crossed from left to right, i.e., in increasing direction. Furthermore, we 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. Furthermore, we show that distributions can be fitted with Johnson probability density function, despite the value of skewness or kurtosis of the distribution.
