论文标题
半融合体重EISENSTEIN系列和Theta Powers的Maass升降机
Maass lifts of half-integral weight Eisenstein series and theta powers
论文作者
论文摘要
在本文中，我们明确构建了模块化形式，其阴影是Eisenstein系列的一系列任意积分和半集成量的重量，级别和角色，cusps $ \ infty $和$ 0 $。作为一种应用，我们为谐波弱的maass形式提供明确的构造，这些形式是hecke eigenforms，是$θ^k，k \ in \ in \ {3，5，7 \} $下的$θ^k，k \ in \ in \ {3，5，7 \} $，其中$θ$是经典的jacobi theta函数。
In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\infty$ and $0$. As an application, we give explicit construction of harmonic weak Maass forms which are Hecke eigenforms and are the preimages of $Θ^k, k \in \{ 3, 5, 7\}$ under the shadow operator, where $Θ$ is the classical Jacobi theta function.
