论文标题
在精致的Kaneko-Zagier猜想中，通用整数指数
On the refined Kaneko-Zagier conjecture for general integer indices
论文作者
论文摘要
精致的Kaneko-Zagier猜想声称，由两种“已完成”有限的多个Zeta值跨越的代数，称为$ \ hat {a} $ - 和$ \ hat {s} $ - mzvs，是同构的。最近，Komori定义了$ \ hat {s} $ - 通用整数的mzvs（即不一定是正面）索引，从而扩展了现有的积极指数定义。鉴于精致的Kaneko-Zagier猜想，Komori的工作表明，这些扩展值与$ \ hat {a} $ -MZV紧密连接，可以以明显的方式定义。在本文中，我们表明，对于一般整数指数，精制的Kaneko-Zagier猜想的概括实际上是从猜想的积极指数中得出的。关键成分是$ \ hat {a} $ - mzvs或$ \ hat {s} $ -MZVS索引的归纳公式，其中至少包含一个非阳性条目。
The refined Kaneko-Zagier conjecture claims that the algebras spanned by two kinds of "completed" finite multiple zeta values, called $\hat{A}$- and $\hat{S}$-MZVs, are isomorphic. Recently, Komori defined $\hat{S}$-MZVs of general integer (i.e., not necessarily positive) indices, extending the existing definition for positive indices. In view of the refined Kaneko-Zagier conjecture, Komori's work suggests that these extended values are closely connected to $\hat{A}$-MZVs of general indices, which can be defined in an obvious way. In this paper, we show that the generalization of the refined Kaneko-Zagier conjecture for general integer indices is actually deduced from the conjecture for positive indices. The key ingredient is an inductive formula for $\hat{A}$-MZVs or $\hat{S}$-MZVs of indices which contain at least one non-positive entry.
