# Shuffle product of finite multiple polylogarithms

Masataka Ono, Shuji Yamamoto

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zagier (in the article “Finite multiple zeta values” in preparation) and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial fraction decomposition which is an idea due to Komori et al. (Math Z 268:993–1011, 2011). As a corollary, we give an algebraic interpretation of our shuffle product.

Original language English 1-14 14 Manuscripta Mathematica https://doi.org/10.1007/s00229-016-0856-9 Accepted/In press - 2016 May 30

### Fingerprint

Polylogarithms
Shuffle
Multiple zeta Values
Analogue
Partial fractions
Preparation
Corollary
Decompose
Interpretation

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Shuffle product of finite multiple polylogarithms. / Ono, Masataka; Yamamoto, Shuji.

In: Manuscripta Mathematica, 30.05.2016, p. 1-14.

Research output: Contribution to journalArticle

Ono, Masataka ; Yamamoto, Shuji. / Shuffle product of finite multiple polylogarithms. In: Manuscripta Mathematica. 2016 ; pp. 1-14.
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abstract = "In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zagier (in the article “Finite multiple zeta values” in preparation) and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial fraction decomposition which is an idea due to Komori et al. (Math Z 268:993–1011, 2011). As a corollary, we give an algebraic interpretation of our shuffle product.",
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