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arXiv · 2603.10376

Algebra Structures of Multiple Eisenstein Series in Positive Characteristic

Ting-Wei Chang·Song-Yun Chen·Fei-Jun Huang·Hung-Chun Tsui
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Abstract

In [CCHT25], the authors introduced multiple Eisenstein series of arbitrary rank in positive characteristic and the $q$-shuffle algebra $\mathcal{E}$ associated with them. In the present paper, we establish a class of linear independence results for multiple Eisenstein series. We also prove that the $q$-shuffle algebra $\mathcal{R}$ of multiple zeta values embeds into the inverse limit of the spaces of multiple Eisenstein series with respect to the rank $r$, and that $\mathcal{E}$ is isomorphic to the tensor square of $\mathcal{R}$. As an application, we show that $\mathcal{E}$ is an associative algebra, thereby verifying the conjecture proposed in [CCHT25]

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Ting-Wei Chang, Song-Yun Chen, Fei-Jun Huang, Hung-Chun Tsui. 2026-03-11. Algebra Structures of Multiple Eisenstein Series in Positive Characteristic. https://arxiv.org/abs/2603.10376

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