论文标题
单数theta升降机的傅里叶雅各比的扩展
The Fourier-Jacobi expansion of the singular theta lift
论文作者
论文摘要
最近，Funke和Hofmann为双还原对$ u（1,1）\ times u（p，q）$，$ p，q \ geq 1 $构建了一个单数theta升降机，用于双还原对$ u（1,1）\ times u（1,1）\ times u（p，q）\ geq 1 $，其输入函数是谐波弱的弱Maass重量$ K = 2-P-Q $。在本文中，我们对电梯的傅立叶 - 雅各比膨胀进行了明确的评估。为此，我们适应了Kudla在他的论文“ Borcherds形式的另一种产品”中提出的一种方法。作为一个应用程序，在情况下，在$ u（p，1）$的情况下，我们恢复了与Borcherds形式相关的新的无限产品扩展，类似于Kudla处理的情况$ O（P，2）$。
Recently, Funke and Hofmann constructed a singular theta lift of Borcherds type for the dual reductive pair $U(1,1)\times U(p,q)$, $p,q\geq 1$, the input functions of which are harmonic weak Maass forms of weight $k= 2-p-q$. In the present paper, we give an explicit evaluation of the Fourier-Jacobi expansion of the lift. For this purpose, we adapt a method introduced by Kudla in his paper 'Another product for a Borcherds form'. As an application, in the case $U(p,1)$ we recover a new infinite product expansion associated to a Borcherds form, analogous to the case $O(p,2)$ treated by Kudla.
