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arXiv · 1706.09136

New functional equations of finite multiple polylogarithms

Masataka Ono
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Abstract

We give a finite analogue of the well-known formula $\mathrm{Li}_{\underbrace{1, \ldots, 1}_n}(t) = \frac{1}{n!}\mathrm{Li}_1(t)^n$ of multiple polylogarithms for any positive integer n by using the shuffle relation of finite multiple polylogarithms of Ono-Yamamoto type. Unlike the usual case, the terms regarded as error terms appear in this formula. As a corollary, we obtain $"t \leftrightarrow 1 - t"$ type new functional equations of finite multiple polylogarithms of Ono-Yamamoto type and Sakugawa-Seki type.

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Masataka Ono. 2017-06-28. New functional equations of finite multiple polylogarithms. https://arxiv.org/abs/1706.09136

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