The digit principle and derivatives of certain <span class="mathjax-formula">$L$</span>-series

David Goss; Bruno Anglès; Tuan Ngo Dac; Federico Pellarin; Floric Tavares Ribeiro

doi:10.5802/pmb.30

The digit principle and derivatives of certain

L

-series
[Principe des chiffres en base

q

et dérivées de certaines séries

L

]

David Goss ; Bruno Anglès ¹ ; Tuan Ngo Dac ² ; Federico Pellarin ³ ; Floric Tavares Ribeiro ¹

¹ Université de Caen Normandie, Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Campus II, Boulevard Maréchal Juin, B.P. 5186, 14032 Caen Cedex, France.
² CNRS and Université de Caen Normandie, Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Campus II, Boulevard Maréchal Juin, B.P. 5186, 14032 Caen Cedex, France.
³ Institut Camille Jordan, UMR 5208, Site de Saint-Etienne, 23 rue du Dr. P. Michelon,42023 Saint-Etienne, France

Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 81-102.

Résumé
Abstract

Dans cet article nous discutons d’un principe des chiffres (« digit principle » ) en base $q$ pour les dérivées de certaines valeurs zêta dans les algèbres de Tate en caractéristique non nulle.

We discuss a digit principle for derivatives of certain $ζ$ -values in Tate algebras of positive characteristic discovered by David Goss.

Reçu le : 2017-09-18
Publié le : 2019-10-15

DOI : 10.5802/pmb.30

Classification : 11M38, 11G09
Mots clés : $L$-values in positive characteristic, log-algebraic theorem, Drinfeld modules

Affiliations des auteurs :

David Goss ; Bruno Anglès ¹ ; Tuan Ngo Dac ² ; Federico Pellarin ³ ; Floric Tavares Ribeiro ¹

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {David Goss and Bruno Angl\`es and Tuan Ngo Dac and Federico Pellarin and Floric Tavares Ribeiro},
     title = {The digit principle and derivatives of certain $L$-series},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
     pages = {81--102},
     publisher = {Presses universitaires de Franche-Comt\'e},
     number = {1},
     year = {2019},
     doi = {10.5802/pmb.30},
     language = {en},
     url = {https://pmb.centre-mersenne.org/articles/10.5802/pmb.30/}
}

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David Goss; Bruno Anglès; Tuan Ngo Dac; Federico Pellarin; Floric Tavares Ribeiro. The digit principle and derivatives of certain $L$-series. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 81-102. doi : 10.5802/pmb.30. https://pmb.centre-mersenne.org/articles/10.5802/pmb.30/

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Publications Mathématiques de Besançon

Algèbre et Théorie des Nombres