Riemann Zeta函数的六阶和

The 6-Order Sums of Riemann Zeta Function

利用概率论与组合数学的方法，研究了与Riemann—zeta函数ζ（k）的部分和ζn（k）有关的一些级数，计算出了一些重要的和式．特别的，Euler的著名结果5ζ（4）=2ζ^2（2）能够从四阶和式直接推出．因此，通过计算全部的11个六阶和式，研究它们之间的非平凡关系，就有可能得到ζ（3）的数值．

We study in this paper certain series involving ζn（k）, which are the partial sums of Riemann-zeta function ζ（k）, by the probabilistic and combinatorial methods, several important sums are evaluated. Specially the known result of Euler 5ζ（4） = 2ζ^2 （2） can .bc derived directly from the three sums of 4-order, and therefore the eleven sums of 6-order evaluated in this paper imply that it is possible to obtain the value of ζ（3） from searching for the nontrivial relation among certain series.