On the algebraic independence of logarithms of Anderson $t$-modules
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916672293568512 |
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| author | Gezmiş, Oğuz Namoijam, Changningphaabi |
| author_facet | Gezmiş, Oğuz Namoijam, Changningphaabi |
| contents | In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson $t$-modules constructed by taking the tensor product of Drinfeld modules of rank $r$ defined over the algebraic closure of the rational function field and their $(r-1)$-st exterior powers with the Carlitz tensor powers. Our results, in the case of the tensor powers of the Carlitz module, generalize the work of Chang and Yu on the algebraic independence of polylogarithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18916 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the algebraic independence of logarithms of Anderson $t$-modules Gezmiş, Oğuz Namoijam, Changningphaabi Number Theory 11G09, 11J93 In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson $t$-modules constructed by taking the tensor product of Drinfeld modules of rank $r$ defined over the algebraic closure of the rational function field and their $(r-1)$-st exterior powers with the Carlitz tensor powers. Our results, in the case of the tensor powers of the Carlitz module, generalize the work of Chang and Yu on the algebraic independence of polylogarithms. |
| title | On the algebraic independence of logarithms of Anderson $t$-modules |
| topic | Number Theory 11G09, 11J93 |
| url | https://arxiv.org/abs/2407.18916 |