On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
Chieh-Yu Chang, Song-Yun Chen, Fei-Jun Huang, Hung-Chun Tsui
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].
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