On Multiple Polylogarithms in Characteristic p: v-Adic Vanishing Versus ∞-Adic Eulerianness. (10th July 2017) - Chang, Chieh-Yu; Mishiba, Yoshinori
Abstract: In this article, we give a simultaneous vanishing principle for the v -adic Carlitz multiple polylogarithms (CMPLs) at algebraic points, where v is a finite place of the rational function field over a finite field. This principle establishes the fact that the v -adic vanishing of CMPLs at algebraic points is equivalent to its ∞ -adic counterpart being Eulerian. This reveals a nontrivial connection between the v -adic and ∞ -adic worlds in positive characteristic.