Quasimodular forms as solutions of modular differential equations
Quasimodular forms as solutions of modular differential equations
复制标题
拟模形式作为模微分方程的解
DOI：
10.1142/s1793042120501158
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发表时间：
2020
影响因子：
0.7
通讯作者：
P. Grabner
中科院分区：
文献类型：
--
作者：
P. Grabner
我们研究quasimodular形式的深度[公式：见文字]，并确定在何种条件下，他们发生的解决方案的模块化微分方程。此外，我们还研究了哪些模微分方程有拟模解。我们利用这些结果研究了M. Kaneko和M.小池进一步。特别是，我们证明了一个猜想，这些作者所述的约数发生在他们的傅立叶展开。
We study quasimodular forms of depth [Formula: see text] 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.