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.
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