Algebraic independence of the Carlitz period and its hyperderivatives

2021/04/06 by Andreas Maurischat, Maurischat, Andreas
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #11J93 #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Receptor Mechanisms and Signaling

paper · doi:10.48550/arxiv.2104.02630

openalex publication_date 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the fundamental period π of the Carlitz module. The main theorem states that the Carlitz period and all its hyperderivatives are algebraically independent over the base field \mathbbF_q(θ). Our approach also reveals a connection of these hyperderivatives with the coordinates of a period lattice generator of the tensor powers of the Carlitz module which was already observed by M. Papanikolas in a yet unpublished paper. Namely, these coordinates can be obtained by explicit polynomial expressions in π and its hyperderivatives. Papanikolas also gave various presentations of these expressions which we also prove here.

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