On $q$-Shuffle Relations for Multiple Eisenstein Series of Arbitrary Rank in Positive Characteristic
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912561504452608 |
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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 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". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $q$-Shuffle Relations for Multiple Eisenstein Series of Arbitrary Rank in Positive Characteristic Chang, Ting-Wei Chen, Song-Yun Huang, Fei-Jun Tsui, Hung-Chun Number Theory 11R58, 11M36 (Primary) 11M32, 11M38 (Secondary) 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". |
| title | On $q$-Shuffle Relations for Multiple Eisenstein Series of Arbitrary Rank in Positive Characteristic |
| topic | Number Theory 11R58, 11M36 (Primary) 11M32, 11M38 (Secondary) |
| url | https://arxiv.org/abs/2504.18879 |