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 $\mathbb{F}_{q}(θ)$ is an $\mathbb{F}_{q}(θ)$-linear combination of finite Carlitz multiple polylogarithms at integral points. It is completely compatible with the formula for Thakur MZV's established in [C14].

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