Linear relations among algebraic points on tensor powers of the Carlitz module
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912738450604032 |
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| author | Chen, Yen-Tsung Harada, Ryotaro |
| author_facet | Chen, Yen-Tsung Harada, Ryotaro |
| contents | In the present paper, we study linear equations on tensor powers of the Carlitz module using the theory of Anderson dual $t$-motives and a detailed analysis of a specific Frobenius difference equation. As an application, we derive some explicit sufficient conditions for the linear independence for Carlitz polylogarithms at algebraic points in both $\infty$-adic and $v$-adic settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14992 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear relations among algebraic points on tensor powers of the Carlitz module Chen, Yen-Tsung Harada, Ryotaro Number Theory 11J72, 11J93, 33E50 In the present paper, we study linear equations on tensor powers of the Carlitz module using the theory of Anderson dual $t$-motives and a detailed analysis of a specific Frobenius difference equation. As an application, we derive some explicit sufficient conditions for the linear independence for Carlitz polylogarithms at algebraic points in both $\infty$-adic and $v$-adic settings. |
| title | Linear relations among algebraic points on tensor powers of the Carlitz module |
| topic | Number Theory 11J72, 11J93, 33E50 |
| url | https://arxiv.org/abs/2307.14992 |