Analytic continuation of multiple polylogarithms in positive characteristic
Number Theory
2022-11-16 v3
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.
Cite
@article{arxiv.2011.00142,
title = {Analytic continuation of multiple polylogarithms in positive characteristic},
author = {Hidekazu Furusho},
journal= {arXiv preprint arXiv:2011.00142},
year = {2022}
}
Comments
23 pages