On finite Carlitz multiple polylogarithms

Chang, Chieh-Yu; Mishiba, Yoshinori

Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 1049-1058.

Dans cet article nous définissons la notion de polylogarithme multiple fini de Carlitz et montrons que chaque valeur de zêta multiple finie définie sûr un corps de fonctions rationnelles ${𝔽}_q\left(\theta \right)$ est une combinaison linéaire des valeurs des polylogarithmes multiples finis de Carlitz evalués en des points entiers. Cela est complètement compatible avec la formule des MZVs de Thakur établie dans [6].

In this paper, we define finite Carlitz multiple polylogarithms and show that every finite multiple zeta value over the rational function field ${𝔽}_q\left(\theta \right)$ is an ${𝔽}_q\left(\theta \right)$-linear combination of finite Carlitz multiple polylogarithms at integral points. It is completely compatible with the formula for Thakur MZV’s established in [6].

Classification : 11R58, 11M38
Mots clés : Finite Carlitz multiple polylogarithms, finite multiple zeta values, Anderson–Thakur polynomials

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