Analytic continuation of multiple polylogarithms in positive characteristic

Abstract

We introduce a method of analytic continuation of Carlitz multiple (star) polylogarithms to the whole space and present a treatment of their branches. 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.