On special L-values of t-modules

Bruno Angles (1) , Tuan Ngo Dac (2, 3) , Floric Ribeiro Tavares (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 ICJ - Institut Camille Jordan
3 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 Angles, Tuan Ngo Dac, Floric Ribeiro Tavares. On special L-values of t-modules. Advances in Mathematics, 2020, 372, ⟨10.1016/j.aim.2020.107313⟩. ⟨hal-01901571v3⟩