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

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

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arXiv · 2504.18879

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

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

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Abstract

In this paper, we define the multiple Eisenstein series of arbitrary rank 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".

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BibTeX RIS

Ting-Wei Chang, Song-Yun Chen, Fei-Jun Huang, Hung-Chun Tsui. 2025-09-01. On $q$-Shuffle Relations for Multiple Eisenstein Series of Arbitrary Rank in Positive Characteristic. https://arxiv.org/abs/2504.18879

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