manuscripta mathematica

, Volume 152, Issue 1–2, pp 153–166 | Cite as

Shuffle product of finite multiple polylogarithms

  • Masataka OnoEmail author
  • Shuji Yamamoto


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.

Mathematics Subject Classification:

Primary 11M32 Secondary 05A19 


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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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsKeio UniversityYokohamaJapan

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