论文标题
来自Poincare系列的一些模块化图的傅立叶系列的零模式
Zero mode of the Fourier series of some modular graphs from Poincare series
论文作者
论文摘要
我们考虑了在环形世界上两个循环模块化图功能的特定线性组合，$ 2S $链接的$ s = 2、3 $和$ 4 $。在每种情况下，它都能满足一个特征值方程，其中涉及$ e_ {2s} $和$ e_s^2 $的源项。从其中删除$ e_ {2s} $和$ e_s^2 $的某些组合时，我们将结果表达为绝对融合的庞加雷系列。这用于以简单的方式计算这些图的傅立叶扩展的零模式的渐近膨胀术语。
We consider specific linear combinations of two loop modular graph functions on the toroidal worldsheet with $2s$ links for $s=2, 3$ and $4$. In each case, it satisfies an eigenvalue equation with source terms involving $E_{2s}$ and $E_s^2$ only. On removing certain combinations of $E_{2s}$ and $E_s^2$ from it, we express the resulting expression as an absolutely convergent Poincare series. This is used to calculate the power behaved terms in the asymptotic expansion of the zero mode of the Fourier expansion of these graphs in a simple manner.
