Explicit evaluation of certain sums of multiple zeta-star values

Shuji Yamamoto

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)


Bowman and Bradley proved an explicit formula for the sum of multiple zeta values whose indices are the sequence (3, 1, 3, 1, ⋯ , 3, 1) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star values and showed that this value is a rational multiple of a power of p. In this paper, we give an explicit formula for the rational part. In addition, we interpret the result as an identity in the harmonic algebra.

Original languageEnglish
Title of host publicationFunctiones et Approximatio, Commentarii Mathematici
PublisherAdam Mickiewicz University Press
Number of pages7
ISBN (Print)9788323226550
Publication statusPublished - 2013



  • Bowman-Bradley theorem
  • Harmonic algebra
  • Kondo-Saito-Tanaka theorem
  • Multiple zeta values
  • Multiple zeta-star values

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Yamamoto, S. (2013). Explicit evaluation of certain sums of multiple zeta-star values. In Functiones et Approximatio, Commentarii Mathematici (2 ed., Vol. 49, pp. 283-289). Adam Mickiewicz University Press. https://doi.org/10.7169/facm/2013.49.2.7