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

N1 - Funding Information: The authors would like to thank the members of the KiPAS-AGNT group for giving us a great environment to study and reading the manuscript carefully, and members of the Department of Mathematics at Keio University for their hospitality. This research was supported in part by JSPS KAKENHI 21674001, 26247004. Publisher Copyright: © 2016, Springer-Verlag Berlin Heidelberg.

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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.

AB - 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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