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arXiv · 2011.00142

Analytic continuation of multiple polylogarithms in positive characteristic

Hidekazu Furusho
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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.

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Hidekazu Furusho. 2020-10-30. Analytic continuation of multiple polylogarithms in positive characteristic. https://doi.org/10.2140/tunis.2022.4.559

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