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2017 Some variations of multiple zeta values
Chan-Liang Chung, Minking Eie
Rocky Mountain J. Math. 47(7): 2107-2131 (2017). DOI: 10.1216/RMJ-2017-47-7-2107

Abstract

In this paper, we build some variations of multiple zeta values and investigate their relations. Among other things, we prove that \[ \sum _{\substack {|\boldsymbol {\alpha }|=m+r\\ 1\leq k_1\lt k_2\lt \cdots \lt k_r}} \!\!\!\!\!\!\!\!k_1^{-\alpha _1}k_2^{-\alpha _2} \cdots k_r^{-\alpha _r}(k_r-p)^{-1} \] can be evaluated as a linear combination of $\zeta (r), \zeta (r-1), \ldots , \zeta (r-p+1)$ for $r\geq p+1$. In particular, for $r\geq 2$, \[ \sum _{\substack {|{\bf \alpha }|=m+r\\ 1\leq k_1\lt k_2\lt \cdots \lt k_r}} \!\!\!\!\!\!\!\!k_1^{-\alpha _1}k_2^{-\alpha _2} \cdots k_r^{-\alpha _r}(k_r-1)^{-1}=\zeta (r), \] which may be compared to the well-known sum formula. A similar discussion leads to the twisted sum formula.

Citation

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Chan-Liang Chung. Minking Eie. "Some variations of multiple zeta values." Rocky Mountain J. Math. 47 (7) 2107 - 2131, 2017. https://doi.org/10.1216/RMJ-2017-47-7-2107

Information

Published: 2017
First available in Project Euclid: 24 December 2017

zbMATH: 06828633
MathSciNet: MR3743707
Digital Object Identifier: 10.1216/RMJ-2017-47-7-2107

Subjects:
Primary: 40B05
Secondary: 11M06, 11M40, 33E20

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 7 • 2017
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