标题： 椭圆模函数$j(τ)$的傅里叶系数和奇异模，重新审视 显示英文标题

标题： The Fourier coefficients and singular moduli of the elliptic modular function $j(τ)$, revisited

摘要： Kaneko公式将椭圆模函数$j$的傅里叶系数表示为奇异模量的有限和。 首次作为一篇短文于1996年发表，它是受Borcherds乘积启发的Zagier工作的结果。 自那时以来，该公式发展成一个更广泛的框架，将模形式的傅里叶系数与模函数的特殊值联系起来，并在各个方向上得到了扩展。 本文综述了这些后续的发展。 显示英文摘要

摘要： Kaneko's formula expresses the Fourier coefficients of the elliptic modular $j$-function as finite sums of singular moduli. First published as a short article in 1996, it was presented as a consequence of Zagier's work inspired by Borcherds products. Since then, the formula has developed into a broader framework that links the Fourier coefficients of modular forms to the special values of modular functions, extending in various directions. This article surveys these subsequent developments.