Functiones et Approximatio Commentarii Mathematici

Restricted sum formula of multiple zeta values

Haiping Yuan and Jianqiang Zhao

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Abstract

The famous sum formula of multiple zeta values (MZV) says that the sum of all MZVs of fixed weight w and depth d is always equal to (w). Hoffman proved a more complicated formula when all the arguments of the MZVs are even numbers. In this paper, we further restrict the arguments to multiples of $4$ and derive a similar sum formula.

Article information

Source
Funct. Approx. Comment. Math., Volume 51, Number 1 (2014), 111-119.

Dates
First available in Project Euclid: 24 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1411564617

Digital Object Identifier
doi:10.7169/facm/2014.51.1.5

Mathematical Reviews number (MathSciNet)
MR3263071

Zentralblatt MATH identifier
1357.11081

Subjects
Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 11B68: Bernoulli and Euler numbers and polynomials

Keywords
multiple zeta values generating functions

Citation

Yuan, Haiping; Zhao, Jianqiang. Restricted sum formula of multiple zeta values. Funct. Approx. Comment. Math. 51 (2014), no. 1, 111--119. doi:10.7169/facm/2014.51.1.5. https://projecteuclid.org/euclid.facm/1411564617


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References

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  • J. Zhao, Restricted sum Formula of alternating Euler sums, arxiv: 1207.5366.