Multiple zeta values vs. multiple zeta-star values

Kentaro Ihara, Jun Kajikawa, Yasuo Ohno, Jun ichi Okuda

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the (q-)multiple zeta values and the (q-)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map between these two classes has a quite interesting algebraic property in a general setting, for example, the compatibility with the harmonic product. We also study several applications of the result.

Original languageEnglish
Pages (from-to)187-208
Number of pages22
JournalJournal of Algebra
Issue number1
Publication statusPublished - 2011 Apr 15
Externally publishedYes


  • Harmonic algebra
  • Multiple zeta values
  • Multiple zeta-star values
  • Q-Series

ASJC Scopus subject areas

  • Algebra and Number Theory


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