AI 中文总结
该研究证明了素数检测拟模形式全Z-模上存在无穷多个通用拉马努金型同余式，且对每个素数p均存在对应算术级数使相关系数被p整除。
AI 中文摘要
我们证明了存在无穷多个拉马努金型同余式，它们在整个素数检测拟模形式的全Z-模上一致成立。特别地，我们证明了对于每个素数p，至少存在一个算术级数An+B，使得每个素数检测拟模形式的系数在该级数中都能被p整除。
英文摘要
We establish the existence of infinitely many Ramanujan-type congruences which hold uniformly for the full $\Z$-module of prime detecting quasimodular forms. In particular, we prove that for every prime $p$, there is at least one arithmetic progression $An+B$ such that every prime-detecting quasimodular form has coefficients divisible by $p$ in this progression.
