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Hung-Chun Tsui

Publications and source records attributed to Hung-Chun Tsui.

4 recordsLinked to original sources
arXiv2026

On $u$-Multiple Zeta Values in Positive Characteristic

In this paper, we introduce the concepts of the $u$-bracket, finite multiple harmonic $u$-series, and $u$-multiple zeta values via the Carlitz module. These objects serve as function field counterparts to the classical theory of $q$-analogs. We prove that the "limits" of finite multiple harmonic $u$-series at Carlitz torsion points yield Thakur's multiple zeta values and finite multiple zeta values over $\mathbb{F}_r(θ)$ from analytic and algebraic perspectives, respectively. This can be regarded as a positive characteristic analog of the results by Bachmann, Takeyama, and Tasaka [BTT18]. Furthermore, we investigate the properties of $u$-multiple zeta values and their expansions, obtaining a family of explicit relations among Thakur's multiple zeta values at both positive and non-positive indices.

math.NT↗
arXiv2026

Algebra Structures of Multiple Eisenstein Series in Positive Characteristic

In [CCHT25], the authors introduced multiple Eisenstein series of arbitrary rank in positive characteristic and the $q$-shuffle algebra $\mathcal{E}$ associated with them. In the present paper, we establish a class of linear independence results for multiple Eisenstein series. We also prove that the $q$-shuffle algebra $\mathcal{R}$ of multiple zeta values embeds into the inverse limit of the spaces of multiple Eisenstein series with respect to the rank $r$, and that $\mathcal{E}$ is isomorphic to the tensor square of $\mathcal{R}$. As an application, we show that $\mathcal{E}$ is an associative algebra, thereby verifying the conjecture proposed in [CCHT25]

math.NT↗
arXiv2025

On $q$-Shuffle Relations for Multiple Eisenstein Series of Arbitrary Rank in Positive Characteristic

In this paper, we define the multiple Eisenstein series of arbitrary rank in positive characteristic, with Thakur's multiple zeta values appearing as the "constant terms" of their expansions in terms of "multiple Goss sums". We show that the multiple Eisenstein series satisfy the same $q$-shuffle relations as the multiple zeta values do, thereby lifting the relations from "values" to "functions".

math.NT↗