In [36], Thakur defines function field analogs of the classical multiple zeta function, namely, and , where is a global function field. Star versions of these functions were further studied by Masri [28]. We prove reduction formulas for these star functions, extend the construction to function field analogs of multiple polylogarithms, and exhibit some formulas for multiple zeta values.
Dans [36], Thakur définit des analogues de la fonction zêta multiple sur les corps de fonctions, et , où est un corps de fonctions global. Les versions étoilées de ces fonctions ont été étudiées par Masri [28]. Nous prouvons des formules de réduction pour ces fonctions étoilées, nous définissons des analogues des polylogarithmes multiples et nous présentons quelques formules pour des valeurs zêta multiples.
Accepted:
Published online:
Classification: 11M41, 11R58, 11T55, 14H05
Keywords: Function field, multiple zeta function, multiple polylogarithms
Author's affiliations:
@article{JTNB_2020__32_2_403_0, author = {Debmalya Basak and Nicolas Degr\'e-Pelletier and Matilde N. Lal{\'\i}n}, title = {Multiple zeta functions and polylogarithms over global function fields}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {403--438}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {32}, number = {2}, year = {2020}, doi = {10.5802/jtnb.1128}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1128/} }
TY - JOUR TI - Multiple zeta functions and polylogarithms over global function fields JO - Journal de Théorie des Nombres de Bordeaux PY - 2020 DA - 2020/// SP - 403 EP - 438 VL - 32 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1128/ UR - https://doi.org/10.5802/jtnb.1128 DO - 10.5802/jtnb.1128 LA - en ID - JTNB_2020__32_2_403_0 ER -
Debmalya Basak; Nicolas Degré-Pelletier; Matilde N. Lalín. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1128/
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