论文标题
磁性（准）模块化形式
Magnetic (quasi-)modular forms
论文作者
论文摘要
A（Folklore？）猜想指出，不存在$ f（τ）= \ sum_ {n = 1}^\ infty a_nq^n \ in q \ mathbb z [[q] $的存在，其中$ q = e^e^{2πiτ} $ a_nq^n/n $在$ q $ - expansion中具有积分系数。 Li和Neururer严格完成的Broadhurst和Zudilin的最新观察结果导致了具有完整性特性的Meromormormormormormormormormormormormormormormor形式。在本说明中，我们从系统的角度研究了算术现象，并讨论了准二型形式的差异封闭环的相关先验扩展。
A (folklore?) conjecture states that no holomorphic modular form $F(τ)=\sum_{n=1}^\infty a_nq^n\in q\mathbb Z[[q]]$ exists, where $q=e^{2πiτ}$, such that its anti-derivative $\sum_{n=1}^\infty a_nq^n/n$ has integral coefficients in the $q$-expansion. A recent observation of Broadhurst and Zudilin, rigorously accomplished by Li and Neururer, led to examples of meromorphic modular forms possessing the integrality property. In this note we investigate the arithmetic phenomenon from a systematic perspective and discuss related transcendental extensions of the differentially closed ring of quasi-modular forms.
