论文标题
部分可观测时空混沌系统的无模型预测
The $D^6 R^4$ interaction as a Poincaré series, and a related shifted convolution sum
论文作者
论文摘要
我们完成了该程序，该程序是在2015年的绿色，米勒和VanHove的论文中启动的，直接构建了字符串理论的自动型解决方案$ d^6 r^4 $ dinaceial方程$（δ-12）f = -e_ {3/2}^2 $ for $ sl（2，\ z）$。该结构是通过庞加莱系列的类型，需要明确评估特定的双重积分。我们还展示了如何使用双迪里奇系列系列来正式得出$ f $ f $傅立叶扩展中出现的一种类型的术语的预测消失，这证实了切斯特，格林，普富，王，王以及杨 - 米尔斯理论激励的猜想（后来又是由fedosova，klinger-logan and ragchenko的proferestion crouts of coint of the and yang-mills the的动机引理。）。
We complete the program, initiated in a 2015 paper of Green, Miller, and Vanhove, of directly constructing the automorphic solution to the string theory $D^6 R^4$ differential equation $(Δ-12)f=-E_{3/2}^2$ for $SL(2,\Z)$. The construction is via a type of Poincaré series, and requires explicitly evaluating a particular double integral. We also show how to use double Dirichlet series to formally derive the predicted vanishing of one type of term appearing in $f$'s Fourier expansion, confirming a conjecture made by Chester, Green, Pufu, Wang, and Wen motivated by Yang-Mills theory (and later proved rigorously by Fedosova, Klinger-Logan, and Radchenko using the Gross-Zagier Holomorphic Projection Lemma.).
