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Analytic continuation of multiple polylogarithms in positive characteristic

Hidekazu Furusho

Vol. 4 (2022), No. 3, 559–586

The aim of this paper is to propose a method of analytic continuation of the Carlitz multiple (star) polylogarithms to the whole space by using Artin–Schreier equations and present a treatment of their branches by introducing the notion of monodromy modules. As applications of this method, we obtain (1) a method of continuation of the logarithms of higher tensor powers of the Carlitz module, (2) the orthogonal property (Chang–Mishiba functional relations), (3) a branch independency of the Eulerian property.

(t-motivic) Carlitz (multiple) (star) polylogarithm, Carlitz module, t-module
Mathematical Subject Classification
Primary: 11R58, 33E50
Received: 29 November 2021
Revised: 3 February 2022
Accepted: 19 February 2022
Published: 9 November 2022
Hidekazu Furusho
Graduate School of Mathematics
Nagoya University
Chikusaku, Nagoya 464-8602