Explicit evaluation of certain sums of multiple zeta-star values

Shuji Yamamoto

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

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
Pages283-289
Number of pages7
Volume49
Edition2
DOIs
Publication statusPublished - 2013

Publication series

NameFunctiones et Approximatio, Commentarii Mathematici
Number2
Volume49
ISSN (Print)02086573
ISSN (Electronic)20809433

Fingerprint

Explicit Formula
Star
Multiple zeta Values
Evaluation
Harmonic
Algebra

Keywords

  • 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). (Functiones et Approximatio, Commentarii Mathematici; Vol. 49, No. 2). https://doi.org/10.7169/facm/2013.49.2.7

Explicit evaluation of certain sums of multiple zeta-star values. / Yamamoto, Shuji.

Functiones et Approximatio, Commentarii Mathematici. Vol. 49 2. ed. 2013. p. 283-289 (Functiones et Approximatio, Commentarii Mathematici; Vol. 49, No. 2).

Research output: Chapter in Book/Report/Conference proceedingChapter

Yamamoto, S 2013, Explicit evaluation of certain sums of multiple zeta-star values. in Functiones et Approximatio, Commentarii Mathematici. 2 edn, vol. 49, Functiones et Approximatio, Commentarii Mathematici, no. 2, vol. 49, pp. 283-289. https://doi.org/10.7169/facm/2013.49.2.7
Yamamoto S. Explicit evaluation of certain sums of multiple zeta-star values. In Functiones et Approximatio, Commentarii Mathematici. 2 ed. Vol. 49. 2013. p. 283-289. (Functiones et Approximatio, Commentarii Mathematici; 2). https://doi.org/10.7169/facm/2013.49.2.7
Yamamoto, Shuji. / Explicit evaluation of certain sums of multiple zeta-star values. Functiones et Approximatio, Commentarii Mathematici. Vol. 49 2. ed. 2013. pp. 283-289 (Functiones et Approximatio, Commentarii Mathematici; 2).
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