论文标题
汽车施瓦茨方程
Automorphic Schwarzian equations
论文作者
论文摘要
本文涉及Schwarz微分方程$ \ {h，τ\} = s \，e_4（τ）$的研究，其中$ e_4 $是重量4 Eisenstein系列和$ S $是一个复杂的参数。特别是，我们确定解决方案$ h $是$ \ mbox {sl} _2（\ mathbb z）$的有限索引子组的$ s $的所有值。我们这样做是使用均值上半平面上的均衡函数理论，以及对$ \ mbox {sl} _2（\ mathbb z）$的表示理论的分析。这也导致了Fuchsian微分方程的解决方案$ y''+s \，e_4 \，y = 0 $。
This paper concerns the study of the Schwarz differential equation $\{h,τ\}=s\,E_4(τ)$ where $E_4$ is the weight 4 Eisenstein series and $s$ is a complex parameter. In particular, we determine all the values of $s$ for which the solutions $h$ are modular functions for a finite index subgroup of $\mbox{SL}_2(\mathbb Z)$. We do so using the theory of equivariant functions on the complex upper-half plane as well as an analysis of the representation theory of $\mbox{SL}_2(\mathbb Z)$. This also leads to the solutions to the Fuchsian differential equation $y''+s\,E_4\,y=0$.
