Typically, a Maass lift is a map from (holomorphic) Jacobi forms of index $1$ to Siegel modular forms of degree $2$ or other kinds of modular forms. In this paper, we construct Maass lifts from weak Jacobi forms to (non-holomorphic) Siegel modular forms of degree $2$ with or without levels and characters, as formal series. By the Koecher principle, the images of our lifts are not holomorphic at cusps, even if the formal series converge. When the level is equal or less than $3$ and the character is trivial, the image of our Maass lift is in the space of meromorphic Siegel modular forms.

中文翻译：

---

Weierstrass℘函数和弱Jacobi形式的Maass提升的推广

通常，Maass升降机是从索引（$ 1 $）的（全同性）Jacobi形式到度数为$ 2 $的Siegel模块化形式或其他类型的模块化形式的映射。在本文中，我们构造了从弱Jacobi形式到（非全同性的）Siegel模块化形式（程度为2 $）的Maass升降机，带或不带水平和字符，为正式系列。根据Koecher原理，即使正式系列收敛，我们的升降机图像也不是全貌。当级别等于或小于$ 3 $且角色不重要时，Maass升降机的图像位于亚纯Siegel模块化形式的空间中。