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arXiv · 2404.16427

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

Daichi Matsuzuki
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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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Daichi Matsuzuki. 2024-04-25. On algebraic independence of Taylor coefficients of certain Anderson-Thakur series. https://arxiv.org/abs/2404.16427

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