Shuffle product of finite multiple polylogarithms

Masataka Ono*, Shuji Yamamoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zagier (in the article “Finite multiple zeta values” in preparation) and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial fraction decomposition which is an idea due to Komori et al. (Math Z 268:993–1011, 2011). As a corollary, we give an algebraic interpretation of our shuffle product.

Original languageEnglish
Pages (from-to)153-166
Number of pages14
JournalManuscripta Mathematica
Issue number1-2
Publication statusPublished - 2017 Jan 1
Externally publishedYes


  • Primary 11M32
  • Secondary 05A19

ASJC Scopus subject areas

  • Mathematics(all)


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