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.