发表机构
Temple University（天普大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究开发周期多项式方法，解释完全椭圆积分矩间已知有理关系，为模形式临界L-值的相关关系提供概念性说明。
AI 中文摘要
我们开发了一种周期多项式方法，用于研究由θ乘积与椭圆积分矩产生的模形式的临界L-值之间的关系。特别地，周期关系为完全椭圆积分矩之间的若干已知有理关系提供了概念性解释，这些关系此前是通过分析或实验方法发现的。
英文摘要
We construct period polynomial relations for finite systems of theta products stable under modular transformations and use them to derive identities among critical $L$-values. Our main example is a three-component theta system of weight $5$, whose coupled period polynomials are determined explicitly and yield new cross-form relations among critical values of the associated eta products. These relations are not consequences of the functional equations of the individual forms. We also develop a weight-$4$ system arising from a quadratic twist of conductor $3$ and obtain relations linking critical values of the original and twisted modular forms. Through modular parametrizations by complete elliptic integrals, these $L$-value identities yield corresponding moment identities. The method gives a unified modular-symbol explanation of several previously known elliptic integral moment relations while producing new critical-value relations between distinct modular forms.
Comments41 pages
