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Chieh-Yu Chang; Yoshinori Mishiba
On finite Carlitz multiple polylogarithms
Journal de théorie des nombres de Bordeaux, 29 no. 3 (2017), p. 1049-1058, doi: 10.5802/jtnb.1011
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Class. Math.: 11R58, 11M38
Keywords: Finite Carlitz multiple polylogarithms, finite multiple zeta values, Anderson–Thakur polynomials

Résumé - 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 [6].

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