摘要
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.