Families of weighted sum formulas for multiple zeta values

Li Guo, Peng Lei, Jianqiang Zhao

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.

Original languageEnglish (US)
Pages (from-to)997-1025
Number of pages29
JournalInternational Journal of Number Theory
Issue number3
StatePublished - May 25 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Bernoulli numbers
  • multiple zeta values
  • symmetric polynomials


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