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arXiv · 2308.05825

A $v$-adic variant of Anderson-Brownawell-Papanikolas linear independence criterion and its application

Yen-Tsung Chen
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Abstract

Let $\overline{k}$ be a fixed algebraic closure of $k$. When the finite place $v$ is of degree one, we show that all $\overline{k}$-linear relations among $v$-adic Carlitz multiple polylogarithms at algebraic points arise from $k$-linear relations among these values of the same weight. As an application, we establish a function field analogue of Furusho-Yamashita's conjecture for $v$-adic multiple zeta values whenever the degree of the place $v$ is one.

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Yen-Tsung Chen. 2023-08-10. A $v$-adic variant of Anderson-Brownawell-Papanikolas linear independence criterion and its application. https://doi.org/10.4310/mrl.251123230910

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