Shuffle product of finite multiple polylogarithms

Masataka Ono; Shuji Yamamoto

doi:10.1007/s00229-016-0856-9

Shuffle product of finite multiple polylogarithms

Masataka Ono, Shuji Yamamoto

Graduate School of Science and Technology

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

3 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
Pages (from-to)	153-166
Number of pages	14
Journal	Manuscripta Mathematica
Volume	152
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-016-0856-9
Publication status	Published - 2017 Jan 1

Keywords

Primary 11M32
Secondary 05A19

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00229-016-0856-9

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AU - Yamamoto, Shuji

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N2 - 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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Shuffle product of finite multiple polylogarithms

Abstract

Keywords

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