On finite Carlitz multiple polylogarithms

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].