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 |
| Pages | 283-289 |
| Number of pages | 7 |
| Volume | 49 |
| Edition | 2 |
| DOIs | |
| Publication status | Published - 2013 |
Publication series
| Name | Functiones et Approximatio, Commentarii Mathematici |
|---|---|
| Number | 2 |
| Volume | 49 |
| ISSN (Print) | 02086573 |
| ISSN (Electronic) | 20809433 |
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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
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 proceeding › Chapter
}
TY - CHAP
T1 - Explicit evaluation of certain sums of multiple zeta-star values
AU - Yamamoto, Shuji
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Bowman-Bradley theorem
KW - Harmonic algebra
KW - Kondo-Saito-Tanaka theorem
KW - Multiple zeta values
KW - Multiple zeta-star values
UR - http://www.scopus.com/inward/record.url?scp=84892945471&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84892945471&partnerID=8YFLogxK
U2 - 10.7169/facm/2013.49.2.7
DO - 10.7169/facm/2013.49.2.7
M3 - Chapter
AN - SCOPUS:84892945471
SN - 9788323226550
VL - 49
T3 - Functiones et Approximatio, Commentarii Mathematici
SP - 283
EP - 289
BT - Functiones et Approximatio, Commentarii Mathematici
ER -