On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result

Abstract: In this paper, we study multiple Eisenstein series (MES) in positive characteristic. By computing and analyzing the t-expansions of MES, we determine the precise "weights" of their coefficients. This framework enables us to establish a graded algebra structure for MES, extending the direct sum result for Thakur's multiple zeta values proved in [Cha14]. Our result may also be viewed as a function field analogue of the corresponding direct sum result of Bachmann and Kanno [BK26].