Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| author | Namoijam, Changningphaabi Papanikolas, Matthew A. |
| author_facet | Namoijam, Changningphaabi Papanikolas, Matthew A. |
| contents | We investigate periods, quasi-periods, logarithms, and quasi-logarithms of Anderson $t$-modules, as well as their hyperderivatives. We develop a comprehensive account of how these values can be obtained through rigid analytic trivializations of abelian and $\mathbf{A}$-finite $t$-modules. To do this we build on the exponentiation theorem of Anderson and investigate quasi-periodic extensions of $t$-modules through Anderson generating functions. By applying these results to prolongation $t$-modules of Maurischat, we integrate hyperderivatives of these values together with previous work of Brownawell and Denis in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_05836 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hyperderivatives of periods and quasi-periods for Anderson $t$-modules Namoijam, Changningphaabi Papanikolas, Matthew A. Number Theory 11G09 (Primary), 11J93, 33E50 (Secondary) We investigate periods, quasi-periods, logarithms, and quasi-logarithms of Anderson $t$-modules, as well as their hyperderivatives. We develop a comprehensive account of how these values can be obtained through rigid analytic trivializations of abelian and $\mathbf{A}$-finite $t$-modules. To do this we build on the exponentiation theorem of Anderson and investigate quasi-periodic extensions of $t$-modules through Anderson generating functions. By applying these results to prolongation $t$-modules of Maurischat, we integrate hyperderivatives of these values together with previous work of Brownawell and Denis in this framework. |
| title | Hyperderivatives of periods and quasi-periods for Anderson $t$-modules |
| topic | Number Theory 11G09 (Primary), 11J93, 33E50 (Secondary) |
| url | https://arxiv.org/abs/2103.05836 |