We survey divisibility properties of the Fourier coefficients of modular functions inspired by Ramanujan. Then using recent results of the generalized Hecke operator on harmonic Maass functions and known divisibility of Fourier coefficients of modular functions, we establish congruence relations of the Fourier coefficients of certain modular functions and mock modular functions of various levels.

中文翻译：

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（模拟）模函数的傅立叶系数和拉马努金的可分性

我们调查了受 Ramanujan 启发的模函数的傅立叶系数的可分性。然后利用广义Hecke算子在调和Maass函数上的最新成果和已知模函数傅里叶系数的可分性，建立了某些模函数的傅里叶系数和各级mock模函数的同余关系。