On finite Carlitz multiple polylogarithms
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 𝔽q(θ) 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 𝔽q(θ) is an 𝔽q(θ)-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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DOI : 10.5802/jtnb.1011
Classification : 11R58, 11M38
Mots-clés : Finite Carlitz multiple polylogarithms, finite multiple zeta values, Anderson–Thakur polynomials

Chieh-Yu Chang 1 ; Yoshinori Mishiba 2

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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Chieh-Yu Chang; Yoshinori Mishiba. On finite Carlitz multiple polylogarithms. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 1049-1058. doi : 10.5802/jtnb.1011. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1011/

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