On algebraic independence of Taylor coefficients of certain Anderson-Thakur series

2024/04/25 by Daichi Matsuzuki, Matsuzuki, Daichi
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2404.16427

openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study algebraic independence problem for the Taylor coefficients of the Anderson-Thakur series arisen as deformation series of positive characteristic multiple zeta values (abbreviated as MZV's). These Taylor coefficients are simply specialization of hyperderivatives of the Anderson-Thakur series. We consider the prolongation of t-motives associated with MZV's, and then determine the dimension of the t-motivic Galois groups in question under certain hypothesis. By using Papanikolas' theory, it enables us to obtain the desired algebraic independence result.

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