Infinite Summation Formulas Involving Riemann-Zeta function

Summation of Hyperharmonic Series

We shall show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. More exactly, we give summation formula for the general hyperharmonic series.

Schur多重ζ函数的Littlewood-Richardson规则

The Littlewood-Richardson rule for Schur multiple zeta functions

本文提出基于对称群子群的Schur多重ζ函数乘积的更精细的Littlewood-Richardson规则。

关于黎曼ζ函数均方值的一个注记

A note on the mean square of the Riemann zeta-function

本文针对黎曼ζ函数均方值的已知结果，提出了一种新的证明方法。

Polylogarithm approaches to Riemann Zeta function zeroes

We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results arise from Euler-Zagier sums given in Bailey, Borwein and Crandall [4] providing new infinite product identities.

黎曼ζ函数 $ζ(s)$ 的一种新表示

A New Representation of the Riemann Zeta Function $ζ(s)$

本文推广了黎曼ζ函数与伯努利数的已知关系，提出了一种以伯努利数嵌套级数表示ζ函数的新公式。