arXiv subjects
Publications and source records attributed to Chan-Liang Chung.
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able to evaluate some special (truncated) sums in terms of Riemann zeta values of different weights.
In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\boldsymbolα)$ and define similarly the multiple star $t$-values as $t^{\star}(\boldsymbolα)$. Then we consider the sum of all such multiple (star) $t$-values of fixed depth and weight with even argument and prove that such a sum can be evaluated when the evaluations of $t(\{2m\}^n)$ and $t^{\star}(\{2m\}^n)$ are clear. We give the evaluations of them in terms of the classical Euler numbers through their generating functions.
For $k\leq n$, let $E(mn,k)$ be the sum of all multiple zeta values of depth $k$ and weight $mn$ with arguments are multiples of $m\geq 2$. More precisely, $E(mn,k)=\sum_{|\boldsymbolα|=n}ζ(mα_1,mα_2,\ldots, mα_k)$. In this paper, we develop a formula to express $E(mn,k)$ in terms of $ζ(\{m\}^p)$ and $ζ^\star(\{m\}^q)$, $0\leq p,q\leq n$. In particular, we settle Genčev's conjecture on the evaluation of $E(4n,k)$ and also evaluate $E(mn,k)$ explicitly for small even $m\leq 8$.