Shuffle product of finite multiple polylogarithms

Masataka Ono; Shuji Yamamoto

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arXiv · 1502.06693

Shuffle product of finite multiple polylogarithms

Masataka Ono·Shuji Yamamoto

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Abstract

In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zaiger and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial fraction decomposition due to Komori-Matsumoto-Tsumura. As a corollary, we give an algebraic interpretation of our shuffle product.

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Masataka Ono, Shuji Yamamoto. 2015-02-24. Shuffle product of finite multiple polylogarithms. https://arxiv.org/abs/1502.06693

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