ON SPECIAL L-VALUES OF t-MODULES

Bruno Anglès (1) , Tuan Ngo Dac (1, 2) , Floric Ribeiro Tavares (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CNRS - Centre National de la Recherche Scientifique

We show that Taelman's conjecture on special L-values of Ander-son t-modules holds for a large class of t-modules. This class contains all mixed A-finite and uniformizable t-modules whose Hodge-Pink weights are at least 1. As a consequence, we deduce various log-algebraicity identities for tensor powers of the Carlitz module, generalizing the work of Anderson-Thakur.

Domaines: Théorie des nombres [math.NT]

Bruno Anglès, Tuan Ngo Dac, Floric Ribeiro Tavares. ON SPECIAL L-VALUES OF t-MODULES. 2018. ⟨hal-01901571v2⟩