Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules

2021/03/17 by Changningphaabi Namoijam, Namoijam, Changningphaabi
Mathematics · #11G09 (Secondary) #11J93 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.09485

openalex publication_date 2021/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine all algebraic relations among all hyperderivatives of the periods, quasi-periods, logarithms, and quasi-logarithms of Drinfeld modules defined over a separable closure of the rational function field. In particular, for periods and logarithms that are linearly independent over the endomorphism ring of the Drinfeld module, we prove the algebraic independence of their hyperderivatives and the hyperderivatives of the corresponding quasi-periods and quasi-logarithms.

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