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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16427 |
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| _version_ | 1866914792953872384 |
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| author | Matsuzuki, Daichi |
| author_facet | Matsuzuki, Daichi |
| contents | We study algebraic independence problem for the Taylor coefficients of the Anderson-Thakur series arisen as deformation series of positive characteristic multiple zeta values (abbreviated as MZV's). These Taylor coefficients are simply specialization of hyperderivatives of the Anderson-Thakur series. We consider the prolongation of t-motives associated with MZV's, and then determine the dimension of the t-motivic Galois groups in question under certain hypothesis. By using Papanikolas' theory, it enables us to obtain the desired algebraic independence result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On algebraic independence of Taylor coefficients of certain Anderson-Thakur series Matsuzuki, Daichi Number Theory We study algebraic independence problem for the Taylor coefficients of the Anderson-Thakur series arisen as deformation series of positive characteristic multiple zeta values (abbreviated as MZV's). These Taylor coefficients are simply specialization of hyperderivatives of the Anderson-Thakur series. We consider the prolongation of t-motives associated with MZV's, and then determine the dimension of the t-motivic Galois groups in question under certain hypothesis. By using Papanikolas' theory, it enables us to obtain the desired algebraic independence result. |
| title | On algebraic independence of Taylor coefficients of certain Anderson-Thakur series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.16427 |