发表机构
Chennai Mathematical Institute; School of Mathematics, Trinity College; Hamilton Mathematical Institute, Trinity College（金奈数学研究所; 都柏林圣三一学院数学学院; 都柏林圣三一学院哈密顿数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过将广义误差函数表示为迭代积分，将广义Appell函数的非全纯完备化转化为模形式的迭代Eichler积分，并应用于A_N根格，与拓扑扭曲杨-米尔斯理论相关。
AI 中文摘要
Appell函数是一大类多变量拟椭圆函数，同时也是高深度模拟模形式的实例。这些函数的一个核心方面是它们的非全纯模完备化。我们之前的工作为一般正定格$\Lambda$发展了Appell函数，并将非全纯完备化用广义误差函数$M_P$表示，这些函数是在$\Lambda\otimes \mathbb{C}$中一个$P$维超平面上的积分。在本续篇中，我们将$M_P$表示为变量$w_j\in \mathbb{H}$的$P$维迭代积分，使得Appell函数的完备化呈现为模形式的迭代Eichler积分的形式。我们将此应用于$A_N$李代数的根格情形，该情形因出现在拓扑扭曲杨-米尔斯理论的配分函数中而特别引人关注。
英文摘要
Appell functions are a large class of multi-variable quasi-elliptic functions, which are also instances of higher depth mock modular forms. A central aspect of these functions is their non-holomorphic modular completion. Our previous work developed Appell functions for a general positive definite lattice $Λ$, and expressed the non-holomorphic completion in terms of the generalized error functions $M_P$, which are integrals over a $P$-dimensional hyperplane in $Λ\otimes \mathbb{C}$. In this sequel, we express $M_P$ as a $P$-dimensional iterated integral of variables $w_j\in \mathbb{H}$, such that the completion of the Appell function takes the form of an iterated Eichler integral of modular forms. We apply this to the case of the root lattice of the $A_N$ Lie algebra, which is of particular interest because of their appearance in partition functions of topological twisted Yang-Mills theories.
Comments30 pages, references
