On some multiple zeta-star values of one-two-three indices

Koji Tasaka, Shuji Yamamoto

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,.., 2. Our identities give analogues of Zagier's evaluation of ζ(2,.., 2, 3, 2,.., 2) and examples of a kind of duality of multiple zeta-star values. Moreover, their generalizations give partial solutions of conjectures proposed by Imatomi, Tanaka, Wakabayashi and the first author.

Original languageEnglish
Pages (from-to)1171-1184
Number of pages14
JournalInternational Journal of Number Theory
Volume9
Issue number5
DOIs
Publication statusPublished - 2013 Aug

Fingerprint

Star
Duality
Strings
Analogue
Partial
Evaluation
Generalization

Keywords

  • Multiple zeta values
  • multiple zeta-star values
  • two-one formula

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On some multiple zeta-star values of one-two-three indices. / Tasaka, Koji; Yamamoto, Shuji.

In: International Journal of Number Theory, Vol. 9, No. 5, 08.2013, p. 1171-1184.

Research output: Contribution to journalArticle

Tasaka, Koji ; Yamamoto, Shuji. / On some multiple zeta-star values of one-two-three indices. In: International Journal of Number Theory. 2013 ; Vol. 9, No. 5. pp. 1171-1184.
@article{2032d7a345aa4550a79504ce7a007fd7,
title = "On some multiple zeta-star values of one-two-three indices",
abstract = "In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,.., 2. Our identities give analogues of Zagier's evaluation of ζ(2,.., 2, 3, 2,.., 2) and examples of a kind of duality of multiple zeta-star values. Moreover, their generalizations give partial solutions of conjectures proposed by Imatomi, Tanaka, Wakabayashi and the first author.",
keywords = "Multiple zeta values, multiple zeta-star values, two-one formula",
author = "Koji Tasaka and Shuji Yamamoto",
year = "2013",
month = "8",
doi = "10.1142/S1793042113500188",
language = "English",
volume = "9",
pages = "1171--1184",
journal = "International Journal of Number Theory",
issn = "1793-0421",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",

}

TY - JOUR

T1 - On some multiple zeta-star values of one-two-three indices

AU - Tasaka, Koji

AU - Yamamoto, Shuji

PY - 2013/8

Y1 - 2013/8

N2 - In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,.., 2. Our identities give analogues of Zagier's evaluation of ζ(2,.., 2, 3, 2,.., 2) and examples of a kind of duality of multiple zeta-star values. Moreover, their generalizations give partial solutions of conjectures proposed by Imatomi, Tanaka, Wakabayashi and the first author.

AB - In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,.., 2. Our identities give analogues of Zagier's evaluation of ζ(2,.., 2, 3, 2,.., 2) and examples of a kind of duality of multiple zeta-star values. Moreover, their generalizations give partial solutions of conjectures proposed by Imatomi, Tanaka, Wakabayashi and the first author.

KW - Multiple zeta values

KW - multiple zeta-star values

KW - two-one formula

UR - http://www.scopus.com/inward/record.url?scp=84876496219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876496219&partnerID=8YFLogxK

U2 - 10.1142/S1793042113500188

DO - 10.1142/S1793042113500188

M3 - Article

AN - SCOPUS:84876496219

VL - 9

SP - 1171

EP - 1184

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 5

ER -