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Abstract
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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.
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Keywords
(t-motivic) Carlitz (multiple) (star) polylogarithm,
Carlitz module, t-module
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Mathematical Subject Classification
Primary: 11R58, 33E50
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Milestones
Received: 29 November 2021
Revised: 3 February 2022
Accepted: 19 February 2022
Published: 9 November 2022
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