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

2004/05/28 by Anatoly N. Kochubei, Kochubei, Anatoly N.
Mathematics · #11G09 #11M38 #11S40 #12H99 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11G09 #msc:11M38 #msc:11S40 #msc:12H99

paper · pdf · doi:10.48550/arxiv.math/0405544

15 pages, LaTeX-2e

arxiv created 2004/05/28 · openalex publication_date 2004/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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