论文标题
与CM Newforms相关的谐波Maass形式
Harmonic Maass forms associated with CM newforms
论文作者
论文摘要
在本文中，我们使用正规化的theta举重来构造与$ξ$ - 操作员下的二进制theta函数相对应的谐波maass形式。结果，我们表明它们的全态部分具有代数傅立叶系数，并具有兼容的Galois作用。作为一种应用，我们证明了与CM Newforms相对应的谐波Maaass形式系数的合理性能，回答了Bruinier，Ono和Rhoades的问题。
In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $ξ$-operator. As a result, we show that their holomorphic parts have algebraic Fourier coefficients, with compatible Galois action. As an application, we prove rationality properties of coefficients of harmonic Maaass forms corresponding to CM newforms, answering a question of Bruinier, Ono and Rhoades.
