Taelman L-values for Drinfeld modules over Tate algebras

Abstract

In the present paper, we investigate 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.

On identities for zeta values in Tate algebras

“…Since their introduction various works have revealed the importance of these zeta values for both their proper interest and their applications to values of the Goss L-functions, characteristic p multiple zeta values, Anderson's log-algebraicity identities, Taelman's units, and Drinfeld modular forms in Tate algebras (see for example [4,6,7,8,9,11,12,14,15,27,28,32]). We should mention that generalizations of these zeta values to various settings have been also conducted (see for example [2,3,22,23,24]).…”