Identities among restricted sums of multiple zeta values

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• 作者：Minking Eie^a ; ¹ ; ^{minking@math.ccu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Tung-Yang Lee^b ; ^{tungyanglee@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 40A25 ; 40B05 ; secondary ; 11M32 ; 33E20
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：164
• 期：Complete
• 页码：208-222
• 全文大小：297 K

文摘

The duality theorem and sum formula [8] are undoubtedly the crucial relations among multiple zeta values. They can be expressed as ζ({1}^p,q+2)=ζ({1}^q,p+2)$\zeta ({\left\{1\right\}}^p,q+2)=\zeta ({\left\{1\right\}}^q,p+2)$ and respectively, where p and q are nonnegative integers, n is a positive integer greater than or equal to r  , and {1}^k${\left\{1\right\}}^k$ is k repetitions of 1.

In this paper, we shall prove a family of identities among restricted sums

This can be regarded as a generalization of the duality theorem and sum formula. The case of r=0$r=0$ just gives the duality theorem. On the other hand, the special case when p=m$p=m$ and q=0$q=0$ corresponds to the identity which is equivalent to the sum formula via the duality ζ({1}^m+r,2)=ζ(m+r+2)$\zeta ({\left\{1\right\}}^{m+r},2)=\zeta (m+r+2)$. Moreover, we also provide a vector version of such identities.