Arithmetic of positive characteristic L-series values in Tate algebras

Bruno Angles (1) , Federico Pellarin (2) , Floric Tavares-Ribeiro (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CTN - Combinatoire, théorie des nombres

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules defined over Tate algebras. This enables us to generalize Anderson's log-algebraicity Theorem and Taelman's Herbrand-Ribet Theorem.

Mots clés: L-series values; Function fields of positive characteristic; unit module; class module; class number formula

Domaines: Théorie des nombres [math.NT]

Bruno Angles, Federico Pellarin, Floric Tavares-Ribeiro. Arithmetic of positive characteristic L-series values in Tate algebras. Compositio Mathematica, 2016, 152 (1), pp.1-61. ⟨hal-00940567v4⟩