Polylogarithms and a Zeta Function for Finite Places of a Function Field

Abstract

We introduce and study new versions of polylogarithms and a zeta function on a completion of ${\mathbb{F}}_q(x)$ at a finite place. The construction is based on the use of the Carlitz differential equations for ${\mathbb{F}}_q$-linear functions.

15 pages, LaTeX-2e