On finite Carlitz multiple polylogarithms

Chang, Chieh-Yu¹ ; Mishiba, Yoshinori²

¹ Department of Mathematics National Tsing Hua University Hsinchu City 30042, Taiwan R.O.C.
² Department of Life, Environment and Materials Science Fukuoka Institute of Technology, Japan

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

Abstract (VO)

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].

Résumé

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].

Détail

Reçu le : 2016-11-08
Révisé le : 2017-05-09
Accepté le : 2017-05-12
Publié le : 2017-12-13

DOI : 10.5802/jtnb.1011

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

Licence : CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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