Klein David, Kupka Jennifer
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany.
Ramanujan J. 2021;56(3):1029-1060. doi: 10.1007/s11139-020-00324-4. Epub 2020 Oct 20.
We present completions of mock theta functions to harmonic weak Maass forms of weight and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight 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.
我们给出了模拟theta函数到权重为的调和弱Maass形式的完备化以及模拟theta函数系数的代数公式。我们给出了几个权重为的调和弱Maass形式，它们的全纯部分是模拟theta函数。利用这些调和弱Maass形式和米尔森theta提升，我们根据奇异模的迹计算出了所出现的模拟theta函数系数的有限代数公式。
