Functiones et Approximatio Commentarii Mathematici

Restricted sum formula of multiple zeta values

Haiping Yuan and Jianqiang Zhao

Full-text: Open access


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

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

First available in Project Euclid: 24 September 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

multiple zeta values generating functions


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.

Export citation


  • L. Euler, Meditationes circa singulare serierum genus, Novi Comm. Acad. Sci. Petropol. 20 (1775), 140–186; reprinted in Opera Omnia, ser. I, vol. 15, B.G. Teubner, Berlin, 1927, 217–267.
  • H. Gangl, M. Kaneko, and D. Zagier, Double zeta values and modular forms, in: Automorphic Forms and Zeta Functions, S. Böcherer et. al. (eds.), World Scientific, Singapore, 2006, 71–106.
  • M.E. Hoffman, On multiple zeta values of even arguments, arxiv: 1205.7051.
  • J. Zhao, Sum formula of multiple Hurwitz zeta values, to appear in Forum Mathematicum, arxiv: 1207.2368.
  • J. Zhao, Restricted sum Formula of alternating Euler sums, arxiv: 1207.5366.