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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Acknowledgments
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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Ono, M., Yamamoto, S. Shuffle product of finite multiple polylogarithms. manuscripta math. 152, 153–166 (2017). https://doi.org/10.1007/s00229-016-0856-9
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DOI: https://doi.org/10.1007/s00229-016-0856-9