We construct bases of the space of harmonic weak Maass forms of weight \(\kappa \in \frac{1}{2}{\mathbb {Z}}\). Using these bases, we obtain a Shintani lift from a positive integral weight harmonic weak Maass form to a half-integral weight harmonic weak Maass form, which reduces to the classical Shintani lift on the space of cusp forms.

中文翻译：

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谐波弱马斯形的空间基础和谐波弱马斯形的Shintani升力

我们构造权重为\（\ kappa \ in \ frac {1} {2} {\ mathbb {Z}} \）的谐波弱马斯形式的空间基础。使用这些基数，我们获得了Shintani升力，从正整数重调和弱Maass形式变为半积分重调和弱Maass形式，这在尖点形式的空间上简化为经典的Shintani升程。