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

Anatoly N. Kochubei
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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.

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Anatoly N. Kochubei. 2004-05-28. Polylogarithms and a Zeta Function for Finite Places of a Function Field. https://arxiv.org/abs/math/0405544

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