论文标题
椭圆形模块化图表格I：身份和生成序列
Elliptic modular graph forms I: Identities and generating series
论文作者
论文摘要
将椭圆模块的图形函数和形式（EMGF）定义为任意图作为模块化图函数和形式的自然概括，并通过在其Kronecker-Eisenstein系列中包括Abelian组的特征而获得的形式。 EMGF的最简单示例是由绿色函数为圆环上的无质量标量场和Zagier单值椭圆聚集体给出的。更复杂的EMGF是由较高属表面对带穿刺的属表面的不分开变性产生的。 EMGF可以等于在Kronecker-Eisenstein系列系数组合的圆盘上多个积分来表示，并且可以组装成生成序列。这些关系被利用以得出全体形态子图还原公式，以及EMGF之间的代数和差异身份及其生成序列。
Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker--Eisenstein series. The simplest examples of eMGFs are given by the Green function for a massless scalar field on the torus and the Zagier single-valued elliptic polylogarithms. More complicated eMGFs are produced by the non-separating degeneration of a higher genus surface to a genus one surface with punctures. eMGFs may equivalently be represented by multiple integrals over the torus of combinations of coefficients of the Kronecker--Eisenstein series, and may be assembled into generating series. These relations are exploited to derive holomorphic subgraph reduction formulas, as well as algebraic and differential identities between eMGFs and their generating series.
