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

^*Corresponding author for this work

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
Externally published	Yes

Keywords

Primary 11M32
Secondary 05A19

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00229-016-0856-9

Cite this

@article{74e556b9f7bf4411ab46dc3813949ad6,

title = "Shuffle product of finite multiple polylogarithms",

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.",

keywords = "Primary 11M32, Secondary 05A19",

author = "Masataka Ono and Shuji Yamamoto",

note = "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: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/s00229-016-0856-9",

language = "English",

volume = "152",

pages = "153--166",

journal = "Manuscripta Mathematica",

issn = "0025-2611",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Shuffle product of finite multiple polylogarithms

AU - Ono, Masataka

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.

PY - 2017/1/1

Y1 - 2017/1/1

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.

KW - Primary 11M32

KW - Secondary 05A19

UR - http://www.scopus.com/inward/record.url?scp=84973109409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84973109409&partnerID=8YFLogxK

U2 - 10.1007/s00229-016-0856-9

DO - 10.1007/s00229-016-0856-9

M3 - Article

AN - SCOPUS:84973109409

SN - 0025-2611

VL - 152

SP - 153

EP - 166

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 1-2

ER -

Shuffle product of finite multiple polylogarithms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this