Special values of Goss L-series attached to Drinfeld modules of rank 2
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 2, pp. 511-552.

Inspired by the classical setting, Goss defined L-series attached to Drinfeld modules. In this paper, for a fixed choice of a power q of a prime number and a given Drinfeld module ϕ of rank 2 with a certain condition on its coefficients, we give explicit formulas for the values of Goss L-series attached to ϕ at positive integers n such that 2n+1q in terms of polylogarithms and coefficients of the logarithm series of ϕ.

Inspiré par le cadre classique, Goss a défini des séries L attachées aux modules de Drinfeld. Dans cet article, pour une puissance fixée q d’un nombre premier et un module de Drinfeld donné ϕ de rang 2 avec une certaine condition sur ses coefficients, nous donnons des formules explicites pour les valeurs de la série L de Goss attachée à ϕ aux entiers positifs n tels que 2n+1q en termes de polylogarithmes et coefficients de la série logarithmique de ϕ.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1168
Classification: 11G09, 11M38
Keywords: Drinfeld modules, $L$-series, $t$-modules
Gezmiş, Oğuz 1

1 National Center for Theoretical Sciences National Taiwan University Taipei, Taiwan R.O.C.
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Gezmiş, Oğuz. Special values of Goss $L$-series attached to Drinfeld modules of rank 2. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 2, pp. 511-552. doi : 10.5802/jtnb.1168. http://archive.numdam.org/articles/10.5802/jtnb.1168/

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