AI 中文总结
针对$\u005cwidehat{\mathcal{Q}}$-多重zeta值，本文提出两类新对偶公式，给出剩余两类$\boldsymbol{p}$进多重zeta值对偶公式的$q$模拟，部分支撑Kaneko--Zagier猜想及其精细化版本。
AI 中文摘要
本文提出了由Takeyama与Tasaka定义的$\u005cwidehat{\mathcal{Q}}$-多重zeta值（简称$\u005cwidehat{\mathcal{Q}}$-MZVs）的两类对偶公式。由于对$\u005cwidehat{\mathcal{Q}}$-MZV取两种不同极限可分别得到$\boldsymbol{p}$进多重zeta值与$t$进多重zeta值，因此找到$\u005cwidehat{\mathcal{Q}}$-MZVs的关系式可部分支撑Kaneko--Zagier猜想及其精细化版本。目前已知$\boldsymbol{p}$进多重zeta值有三类对偶公式，其中一类的$q$模拟已由Takeyama和Tasaka研究。本文给出了剩余两类$\boldsymbol{p}$进多重zeta值对偶公式的$q$模拟。
英文摘要
In this paper, we introduce two duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values ($\widehat{\mathcal{Q}}$-MZVs for short) which are defined by Takeyama and Tasaka. Since taking two different limits of $\widehat{\mathcal{Q}}$-MZV recovers the $\boldsymbol{p}$-adic multiple zeta value and the $t$-adic multiple zeta value respectively, finding the relation of $\widehat{\mathcal{Q}}$-MZVs partially supports the Kaneko--Zagier conjecture and its refined version. Currently, three types of duality formulas for the $\boldsymbol{p}$-adic multiple zeta values are known, and for one of them, the $q$-analogue was studied by Takeyama and Tasaka. We present $q$-analogues of the remaining two duality formulas for the $\boldsymbol{p}$-adic multiple zeta values.
Comments14 pages
