论文标题
组合多艾森斯坦系列
Combinatorial multiple Eisenstein series
论文作者
论文摘要
我们构建了一个由$ q $ series的家族，具有合理系数，满足扩展双层式方程的变体，该方程是给定的$ \ m athbb {q} $的升降机 - 扩展双层式方程的有价值解决方案。这些$ Q $ - 系列将称为Combinatorial（Bi-）多个Eisenstein系列，在深度为Eisenstein系列中。组合多个Eisenstein系列可以看作是给定的$ \ Mathbb {q} $之间的插值 - 扩展双层式方程的有价值解决方案（如$ Q \ rightArrow 0 $）和多个Zeta值（作为$ Q \ Q \ rightArrow 1 $）。特别是，它们是与模块化形式密切相关的多个Zeta值的$ Q $ - 纳分子。他们的定义灵感来自Gangl-Kaneko-Zagier引入的多个Eisenstein系列的傅立叶扩展。我们的明确构造是在其生成系列级别上完成的，我们表明这是一个所谓的对称和交换不变的。
We construct a family of $q$-series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given $\mathbb{Q}$-valued solution of the extended double shuffle equations. These $q$-series will be called combinatorial (bi-)multiple Eisenstein series, and in depth one they are given by Eisenstein series. The combinatorial multiple Eisenstein series can be seen as an interpolation between the given $\mathbb{Q}$-valued solution of the extended double shuffle equations (as $q\rightarrow 0$) and multiple zeta values (as $q\rightarrow 1$). In particular, they are $q$-analogues of multiple zeta values closely related to modular forms. Their definition is inspired by the Fourier expansion of multiple Eisenstein series introduced by Gangl-Kaneko-Zagier. Our explicit construction is done on the level of their generating series, which we show to be a so-called symmetril and swap invariant bimould.
