论文标题
使用三个和四个长度的多个谐波总和进行一些一致性
On some congruences using multiple harmonic sums of length three and four
论文作者
论文摘要
在本文中，我们确定总和$ \ sum_ {j = 1}^{p-1} \ frac {h_j^{（s_1）} h_j^{（s_3）}} {J^{s_2}}} $ \ sum_ {j = 1}^{p-1} \ frac {h_j^{（s_1）} h_j^{（s_3）} h_j^{（s_4）}} {J^{j^{s_2}}}}这是通过使用长度三和四的多个谐波总和以及许多其他结果来完成的。此外，我们恢复了Z.-W Sun提出的三个一致性，后来由作者本人和R.Meštrović解决。
In the present paper, we determine the sums $\sum_{j=1}^{p-1}\frac{H_j^{(s_1)}H_j^{(s_3)}}{j^{s_2}}$ and $\sum_{j=1}^{p-1}\frac{H_j^{(s_1)}H_j^{(s_3)}H_j^{(s_4)}}{j^{s_2}}$ modulo $p$ and modulo $p^2$ in certain cases. This is done by using multiple harmonic sums of length three and four, as well as, many other results. In addition, We recover three congruences conjectured by Z.-W Sun and solved later by the author himself and R. Meštrović.
