Algebra Structures of Multiple Eisenstein Series in Positive Characteristic
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914384931979264 |
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| author | Chang, Ting-Wei Chen, Song-Yun Huang, Fei-Jun Tsui, Hung-Chun |
| author_facet | Chang, Ting-Wei Chen, Song-Yun Huang, Fei-Jun Tsui, Hung-Chun |
| contents | 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] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10376 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebra Structures of Multiple Eisenstein Series in Positive Characteristic Chang, Ting-Wei Chen, Song-Yun Huang, Fei-Jun Tsui, Hung-Chun Number Theory Primary 11M32, Secondary 11M36, 11M38, 11R58 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] |
| title | Algebra Structures of Multiple Eisenstein Series in Positive Characteristic |
| topic | Number Theory Primary 11M32, Secondary 11M36, 11M38, 11R58 |
| url | https://arxiv.org/abs/2603.10376 |