Multiple zeta values vs. multiple zeta-star values

Kentaro Ihara; Jun Kajikawa; Yasuo Ohno; Jun ichi Okuda

doi:10.1016/j.jalgebra.2010.12.029

Multiple zeta values vs. multiple zeta-star values

Kentaro Ihara, Jun Kajikawa, Yasuo Ohno, Jun ichi Okuda

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

Abstract

We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the (q-)multiple zeta values and the (q-)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map between these two classes has a quite interesting algebraic property in a general setting, for example, the compatibility with the harmonic product. We also study several applications of the result.

Original language	English
Pages (from-to)	187-208
Number of pages	22
Journal	Journal of Algebra
Volume	332
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2010.12.029
Publication status	Published - 2011 Apr 15
Externally published	Yes

Keywords

Harmonic algebra
Multiple zeta values
Multiple zeta-star values
Q-Series

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2010.12.029

Cite this

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title = "Multiple zeta values vs. multiple zeta-star values",

abstract = "We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the (q-)multiple zeta values and the (q-)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map between these two classes has a quite interesting algebraic property in a general setting, for example, the compatibility with the harmonic product. We also study several applications of the result.",

keywords = "Harmonic algebra, Multiple zeta values, Multiple zeta-star values, Q-Series",

author = "Kentaro Ihara and Jun Kajikawa and Yasuo Ohno and Okuda, {Jun ichi}",

note = "Funding Information: E-mail addresses: ihara@postech.ac.kr (K. Ihara), kajikawa@ikuei.ac.jp (J. Kajikawa), ohno@math.kindai.ac.jp (Y. Ohno). URL: http://crosstrust.co.jp/ (J. Okuda). 1 The author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) (No. 2010-0029638). 2 The author is supported by JSPS Grant-in-Aid No. 20540033.",

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doi = "10.1016/j.jalgebra.2010.12.029",

language = "English",

volume = "332",

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journal = "Journal of Algebra",

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AU - Ihara, Kentaro

AU - Kajikawa, Jun

AU - Ohno, Yasuo

AU - Okuda, Jun ichi

N1 - Funding Information: E-mail addresses: ihara@postech.ac.kr (K. Ihara), kajikawa@ikuei.ac.jp (J. Kajikawa), ohno@math.kindai.ac.jp (Y. Ohno). URL: http://crosstrust.co.jp/ (J. Okuda). 1 The author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) (No. 2010-0029638). 2 The author is supported by JSPS Grant-in-Aid No. 20540033.

PY - 2011/4/15

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N2 - We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the (q-)multiple zeta values and the (q-)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map between these two classes has a quite interesting algebraic property in a general setting, for example, the compatibility with the harmonic product. We also study several applications of the result.

AB - We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the (q-)multiple zeta values and the (q-)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map between these two classes has a quite interesting algebraic property in a general setting, for example, the compatibility with the harmonic product. We also study several applications of the result.

KW - Harmonic algebra

KW - Multiple zeta values

KW - Multiple zeta-star values

KW - Q-Series

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JF - Journal of Algebra

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ER -

Multiple zeta values vs. multiple zeta-star values

Abstract

Keywords

ASJC Scopus subject areas

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