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arXiv · 2610.25063

Graded Structures of $v$-adic Carlitz Multiple Polylogarithms and $v$-adic Multiple Zeta Values

Hung-Chun Tsui
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Abstract

In this paper, we study $v$-adic Carlitz multiple polylogarithms and $v$-adic multiple zeta values. We prove that, for every finite place $v$ of $\mathbb{F}_q(θ)$, the natural weight gives a graded structure on the algebras generated by these values. Moreover, we show that every $\overline{\mathbb{F}_q(θ)}$-linear relation among these values arises from an $\mathbb{F}_q(θ)$-linear relation. In particular, our results establish a function field analogue of the Furusho-Yamashita direct sum conjecture and extend Chen's work from finite places of degree one to arbitrary finite places.

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BibTeXRIS

Hung-Chun Tsui. 2026-10-18. Graded Structures of $v$-adic Carlitz Multiple Polylogarithms and $v$-adic Multiple Zeta Values. https://arxiv.org/abs/2610.25063

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