Multiple zeta functions and polylogarithms over global function fields
Journal de théorie des nombres de Bordeaux, Volume 32 (2020) no. 2, pp. 403-438.

In [36], Thakur defines function field analogs of the classical multiple zeta function, namely, ζ d (𝔽 q [T];s 1 ,,s d ) and ζ d (K;s 1 ,,s d ), where K 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, ζ d (𝔽 q [T];s 1 ,,s d ) et ζ d (K;s 1 ,,s d ), où K 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.

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DOI: 10.5802/jtnb.1128
Classification: 11M41, 11R58, 11T55, 14H05
Keywords: Function field, multiple zeta function, multiple polylogarithms
Basak, Debmalya 1; Degré-Pelletier, Nicolas 2; Lalín, Matilde N. 2

1 Indian Institute of Science Education and Research (IISER), Kolkata, Mohanpur, West Bengal 741246, India
2 Université de Montréal, Pavillon André-Aisenstadt, Dépt. de mathématiques et de statistique, CP 6128, succ. Centre-ville Montréal, Québec, H3C 3J7, Canada
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Basak, Debmalya; Degré-Pelletier, Nicolas; Lalín, Matilde N. 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. http://archive.numdam.org/articles/10.5802/jtnb.1128/

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