We present completions of mock theta functions to harmonic weak Maass forms of weight \(\nicefrac {1}{2}\) and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight \(\nicefrac {1}{2}\) that have mock theta functions as their holomorphic part. Using these harmonic weak Maass forms and the Millson theta lift, we compute finite algebraic formulas for the coefficients of the appearing mock theta functions in terms of traces of singular moduli.

中文翻译：

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拉马努金模拟 theta 函数系数的补全和代数公式

我们提出了模拟 theta 函数对权重\(\nicefrac {1}{2}\) 的谐波弱 Maass 形式和模拟 theta 函数系数的代数公式的完成。我们给出了几种谐波弱 Maass 形式的权重\(\nicefrac {1}{2}\)，它们具有模拟 theta 函数作为它们的全纯部分。使用这些谐波弱 Maass 形式和 Millson theta 提升，我们根据奇异模的迹线计算出现的模拟 theta 函数的系数的有限代数公式。