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
In this paper, we define finite Carlitz multiple polylogarithms and show that every finite multiple zeta value over the rational function field
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Mots-clés : Finite Carlitz multiple polylogarithms, finite multiple zeta values, Anderson–Thakur polynomials
Chieh-Yu Chang 1 ; Yoshinori Mishiba 2

@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/} }
TY - JOUR AU - Chieh-Yu Chang AU - Yoshinori Mishiba TI - On finite Carlitz multiple polylogarithms JO - Journal de théorie des nombres de Bordeaux PY - 2017 SP - 1049 EP - 1058 VL - 29 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1011/ DO - 10.5802/jtnb.1011 LA - en ID - JTNB_2017__29_3_1049_0 ER -
%0 Journal Article %A Chieh-Yu Chang %A Yoshinori Mishiba %T On finite Carlitz multiple polylogarithms %J Journal de théorie des nombres de Bordeaux %D 2017 %P 1049-1058 %V 29 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1011/ %R 10.5802/jtnb.1011 %G en %F JTNB_2017__29_3_1049_0
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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- Multiple zeta functions and polylogarithms over global function fields, Journal de Théorie des Nombres de Bordeaux, Volume 32 (2020) no. 2, pp. 403-438 | DOI:10.5802/jtnb.1128 | Zbl:1465.11181
- On finite Carlitz multiple polylogarithms, Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 1049-1058 | DOI:10.5802/jtnb.1011 | Zbl:1430.11125
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