A class formula for L-series in positive characteristic
Annales de l'Institut Fourier, Volume 72 (2022) no. 3, pp. 1149-1183.

We prove a formula for special L-values of Anderson modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of L-series.

Nous prouvons une formule pour les valeurs spéciales des séries L associées aux modules d’Anderson, cette formule étant un analogue de la formule analytique du nombre de classes. Nous appliquons nos résultats à deux types de fonctions L.

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DOI: 10.5802/aif.3512
Classification: 11G09, 11M38, 11R58, 11R60
Keywords: Anderson modules, tensor powers of the Carlitz module, Goss $L$-series, class number formula
Mot clés : Modules d’Anderson, puissances tensorielles du module de Carlitz, fonctions $L$ de Goss, formule analytique du nombre de classes
Demeslay, Florent 1

1 LMNO, CNRS UMR 6139 Université de Caen 14032 Caen cedex (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Demeslay, Florent. A class formula for $L$-series in positive characteristic. Annales de l'Institut Fourier, Volume 72 (2022) no. 3, pp. 1149-1183. doi : 10.5802/aif.3512. https://aif.centre-mersenne.org/articles/10.5802/aif.3512/

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