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The digit principle and derivatives of certain L-series
David Goss; Bruno Anglès1; Tuan Ngo Dac2; Federico Pellarin3; Floric Tavares Ribeiro1
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.

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

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.

Received:
Published online:
DOI: 10.5802/pmb.30
Classification: 11M38, 11G09
Keywords: $L$-values in positive characteristic, log-algebraic theorem, Drinfeld modules

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
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
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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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