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 language | English |
|---|---|
| Title of host publication | Functiones et Approximatio, Commentarii Mathematici |
| Publisher | Adam Mickiewicz University Press |
| Pages | 283-289 |
| Number of pages | 7 |
| Volume | 49 |
| Edition | 2 |
| ISBN (Print) | 9788323226550 |
| DOIs | |
| Publication status | Published - 2013 |
Keywords
- Bowman-Bradley theorem
- Harmonic algebra
- Kondo-Saito-Tanaka theorem
- Multiple zeta values
- Multiple zeta-star values
ASJC Scopus subject areas
- Mathematics(all)
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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