We prove a formula for special -values of Anderson modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of -series.
Nous prouvons une formule pour les valeurs spéciales des séries 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 .
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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
@article{AIF_2022__72_3_1149_0, author = {Demeslay, Florent}, title = {A class formula for $L$-series in positive characteristic}, journal = {Annales de l'Institut Fourier}, pages = {1149--1183}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {3}, year = {2022}, doi = {10.5802/aif.3512}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3512/} }
TY - JOUR AU - Demeslay, Florent TI - A class formula for $L$-series in positive characteristic JO - Annales de l'Institut Fourier PY - 2022 SP - 1149 EP - 1183 VL - 72 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3512/ DO - 10.5802/aif.3512 LA - en ID - AIF_2022__72_3_1149_0 ER -
%0 Journal Article %A Demeslay, Florent %T A class formula for $L$-series in positive characteristic %J Annales de l'Institut Fourier %D 2022 %P 1149-1183 %V 72 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3512/ %R 10.5802/aif.3512 %G en %F AIF_2022__72_3_1149_0
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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