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

2021/03/10 by Changningphaabi Namoijam, Namoijam, Changningphaabi, Matthew A. Papanikolas +1
Chemistry · Mathematics · #11G09 (Primary) #11J93 #33E50 (Secondary) #FOS: Mathematics #Ferrocene Chemistry and Applications #Finite Group Theory Research #Number Theory (math.NT) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2103.05836

openalex publication_date 2021/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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