Abstract:

In 2012, Pellarin defined an L-series which can be seen as a deformation of Goss's L-series. In order to give new identities for Pellarin L-Series, Anglès, Pellarin and Tavares Ribeiro introduced Drinfeld modules over Tate algebras and also generalized the theory of Taelman for Drinfeld modules of rank 1 over Tate algebras. Later on, Anglès and Tavares Ribeiro expanded the theory for the special type of Drinfeld modules of arbitrary rank over Tate algebras. In this talk, we investigate Taelman L-values corresponding to Drinfeld modules over Tate algebras of arbitrary rank. Using our results, we also introduce an L-series which can be seen as a generalization of Pellarin L-series.