论文标题
计算$ j $功能的隔离系数
Computing isolated coefficients of the $j$-function
论文作者
论文摘要
我们考虑了在椭圆模块函数$ j（τ）$的傅立叶系列中有效计算隔离系数$ c_n $的问题。我们表明，具有复杂性$ n^{1+o（1）} $的混合数值模块化方法在实践上是有效的。作为一个应用程序，我们找到了$ c_n $的前几个值，该值首次出现在$ n = 457871 $。
We consider the problem of efficiently computing isolated coefficients $c_n$ in the Fourier series of the elliptic modular function $j(τ)$. We show that a hybrid numerical-modular method with complexity $n^{1+o(1)}$ is efficient in practice. As an application, we locate the first few values of $c_n$ that are prime, the first occurring at $n = 457871$.
