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.
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.
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Mots-clés : Function field, multiple zeta function, multiple polylogarithms
Debmalya Basak 1 ; Nicolas Degré-Pelletier 2 ; Matilde N. Lalín 2
@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 AU - Debmalya Basak AU - Nicolas Degré-Pelletier AU - Matilde N. Lalín TI - Multiple zeta functions and polylogarithms over global function fields JO - Journal de théorie des nombres de Bordeaux PY - 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/ DO - 10.5802/jtnb.1128 LA - en ID - JTNB_2020__32_2_403_0 ER -
%0 Journal Article %A Debmalya Basak %A Nicolas Degré-Pelletier %A Matilde N. Lalín %T Multiple zeta functions and polylogarithms over global function fields %J Journal de théorie des nombres de Bordeaux %D 2020 %P 403-438 %V 32 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1128/ %R 10.5802/jtnb.1128 %G en %F JTNB_2020__32_2_403_0
Debmalya Basak; Nicolas Degré-Pelletier; Matilde N. Lalín. Multiple zeta functions and polylogarithms over global function fields. Journal de théorie des nombres de Bordeaux, Tome 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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