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arXiv · 2103.05836

Hyperderivatives of periods and quasi-periods for Anderson $t$-modules

Changningphaabi Namoijam·Matthew A. Papanikolas
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Abstract

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.

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Changningphaabi Namoijam, Matthew A. Papanikolas. 2021-03-10. Hyperderivatives of periods and quasi-periods for Anderson $t$-modules. https://doi.org/10.1090/memo/1517

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