On finite Carlitz multiple polylogarithms

Abstract

In this paper, we define finite Carlitz multiple polylogarithms and show that every finite multiple zeta value over the rational function field ${\mathbb{F}}_q(\theta )$ is an ${\mathbb{F}}_q(\theta )$-linear combination of finite Carlitz multiple polylogarithms at integral points. It is completely compatible with the formula for Thakur MZV's established in [C14].

arXiv comment8 pages

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