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

Li Guo, Bingyong Xie

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)46-77
Number of pages32
JournalJournal of Algebra
Volume380
DOIs
StatePublished - Apr 5 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Double shuffle relation
  • Euler's decomposition formula
  • Multiple polylogarithm values
  • Multiple zeta values

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