English

Weighted sum formula for multiple zeta values

Number Theory 2010-03-18 v1 Commutative Algebra

Abstract

The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler's formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions.

Keywords

Cite

@article{arxiv.0809.5110,
  title  = {Weighted sum formula for multiple zeta values},
  author = {Li Guo and Bingyong Xie},
  journal= {arXiv preprint arXiv:0809.5110},
  year   = {2010}
}

Comments

18 pages

R2 v1 2026-06-21T11:25:30.068Z