论文标题
多个谐波$ q $ sums和广义有限/对称的多重Zeta值的超级荣誉
Supercongruences of multiple harmonic $q$-sums and generalized finite/symmetric multiple zeta values
论文作者
论文摘要
kaneko- Zagier猜想描述了有限的多个Zeta值与对称的多个Zeta值之间的对应关系。它的精制版本由Jarossay，Rosen和Ono-Seki-yamamoto建立。在本文中，我们通过研究多个谐波$ q $ - sums来阐明这些猜想。我们表明，（广义）有限/对称的多重Zeta值是通过取代数/分析限制的多个谐波$ q $ sums来获得的。作为应用，给出了广义有限/对称的多个Zeta值的逆转，二元性和循环总和公式的新证明。
The Kaneko--Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossay, Rosen and Ono--Seki--Yamamoto. In this paper, we explicate these conjectures through studies of multiple harmonic $q$-sums. We show that the (generalized) finite/symmetric multiple zeta value are obtained by taking an algebraic/analytic limit of multiple harmonic $q$-sums. As applications, new proofs of reversal, duality and cyclic sum formulas for the generalized finite/symmetric multiple zeta values are given.
