English

Explicit double shuffle relations and a generalization of Euler's decomposition formula

Number Theory 2014-10-07 v1 Commutative Algebra Combinatorics Rings and Algebras

Abstract

We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known decomposition formula of Euler that expresses the product of two Riemann zeta values as a sum of double zeta values to a formula that expresses the product of two multiple polylogarithm values as a sum of other multiple polylogarithm values.

Keywords

Cite

@article{arxiv.0808.2618,
  title  = {Explicit double shuffle relations and a generalization of Euler's decomposition formula},
  author = {Li Guo and Bingyong Xie},
  journal= {arXiv preprint arXiv:0808.2618},
  year   = {2014}
}

Comments

29 pages

R2 v1 2026-06-21T11:12:01.989Z