Arithmetic of positive characteristic L-series values in Tate algebras

Bruno Angles, Federico Pellarin, Floric Tavares-Ribeiro

Published 2014-02-01, updated 2015-05-26Version 4

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.