On $q$-Shuffle Relations for Multiple Eisenstein Series in Positive Characteristic

Abstract: In this paper, we define the multiple Eisenstein series in positive characteristic, with Thakur's multiple zeta values appearing as the "constant terms" of their expansions in terms of "multiple Goss sums". We show that the multiple Eisenstein series satisfy the same $q$-shuffle relations as the multiple zeta values do, thereby lifting the relations from "values" to "functions".