Abstract We give an asymptotic formula for traces of weak Maass forms at CM points with an effective bound on the error term. Upon specializing to the modular j-function, we deduce such a result for traces of singular moduli. Due to work of Zagier, and Bringmann and Ono, these traces of weak Maass forms at CM points appear as Fourier coefficients of half-integral weight weakly holomorphic modular forms. Hence, our results give effective upper bounds for these Fourier coefficients.

中文翻译：

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奇异模迹的有效界限

摘要 我们给出了在 CM 点处的弱 Maass 形式迹的渐近公式，并在误差项上有一个有效的界限。在专门研究模 j 函数后，我们针对奇异模的迹推导出这样的结果。由于 Zagier、Bringmann 和 Ono 的工作，CM 点处的这些弱 Maass 形式的迹线表现为半积分权弱全纯模形式的傅立叶系数。因此，我们的结果给出了这些傅立叶系数的有效上限。