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 𝔽 q (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 𝔽 q (θ) is an 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 [6].

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DOI : https://doi.org/10.5802/jtnb.1011
Classification : 11R58,  11M38
Mots clés : Finite Carlitz multiple polylogarithms, finite multiple zeta values, Anderson–Thakur polynomials
@article{JTNB_2017__29_3_1049_0,
     author = {Chieh-Yu Chang and Yoshinori Mishiba},
     title = {On finite {Carlitz} multiple polylogarithms},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {1049--1058},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {3},
     year = {2017},
     doi = {10.5802/jtnb.1011},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1011/}
}
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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