Analytic continuation of multiple polylogarithms in positive characteristic

Abstract

Our aim of this paper is to propose a method of analytic continuation of Carlitz multiple (star) polylogarithms to the whole space by using Artin-Schreier equation 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 Carlitz module, (2) the orthogonal property (Chang-Mishiba functional relations), (3) a branch independency of the Eulerian property.

arXiv comment23 pages

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Cited by in corpus (2)

• On Furusho's analytic continuation of Drinfeld logarithms
• Analytic continuation of Kochubei multiple polylogarithms and its applications