论文标题
作为模块化差分方程的溶液的准排相式形式
Quasimodular forms as solutions of Modular differential equations
论文作者
论文摘要
我们研究深度$ \ leq4 $的准排相形式，并确定它们作为模块化微分方程的解决方案所发生的条件。此外，我们研究哪些模块化微分方程具有准地模溶液。我们使用这些结果来研究M. Kaneko和M. Koike进一步提出的极端准排相式形式。尤其是，我们证明了这些作者关于在其傅立叶扩张中发生的分母的分裂所指出的。
We study quasimodular forms of depth $\leq4$ and determine under which conditions they occur as solutions of modular differential equations. Furthermore, we study which modular differential equations have quasimodular solutions. We use these results to investigate extremal quasimodular forms as introduced by M. Kaneko and M. Koike further. Especially, we prove a conjecture stated by these authors concerning the divisors of the denominators occurring in their Fourier expansion.
