Taelman L-Values for Drinfeld Modules over Tate Algebras

TL;DR

This paper explores Taelman L-values for Drinfeld modules over Tate algebras of any rank and introduces a generalized L-series extending Pellarin's work, enhancing understanding of function field arithmetic.

Contribution

It introduces a new L-series over Tate algebras that generalizes Pellarin L-series and analyzes Taelman L-values for Drinfeld modules of arbitrary rank.

Findings

Defined a convergent L-series in Tate algebras

Extended Pellarin L-series to a broader setting

Provided new insights into Drinfeld modules over Tate algebras

Abstract

In the present paper, we analyze Taelman L-values corresponding to Drinfeld modules over Tate algebras of arbitrary rank. Using our results, we also introduce an L-series converging in Tate algebras which can be seen as a generalization of Pellarin L-series.