Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 1337–1356 | Cite as

Weighted sum formulas of multiple zeta values with even arguments

  • Zhonghua LiEmail author
  • Chen Qin


We prove a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of the arguments. These weighted sum formulas for the zeta values and for the multiple zeta values were conjectured by L. Guo, P. Lei and J. Zhao.


Multiple zeta values Multiple zeta-star values Bernoulli numbers Weighted sum formulas 

Mathematics Subject Classification

11M32 11B68 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesTongji UniversityShanghaiChina

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