On finite Carlitz multiple polylogarithms
Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 1049-1058.

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].

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].

Published online:
DOI: 10.5802/jtnb.1011
Classification: 11R58, 11M38
Keywords: 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
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Chieh-Yu Chang; Yoshinori Mishiba. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1011/

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