论文标题
截短的Siegel-Weil配方和Borcherds形式
A truncated Siegel-Weil formula and Borcherds forms
论文作者
论文摘要
在本文中，我们使用gan-qiu-takeda的正规化siegel-weil公式来获得theta函数积分在截短的模块化曲线上的表达。我们将此结果应用于Borcherds形式对数的截断模块曲线上的积分，并明确描述其渐近行为，尤其是收敛性和不同的贡献。结果为Kudla对Borcherds形式的积分的工作提供了补充，该局限性局限于应用程序的范围。
In this paper we use the regularized Siegel-Weil formula of Gan-Qiu-Takeda to obtain an expression of the integral of the theta function over the truncated modular curve. We apply this result to express the integral over the truncated modular curve of the logarithm of the Borcherds form and we describe explicitly its asymptotic behaviour, and in particular the convergent and divergent contributions. The result provides a complement to the work of Kudla on integrals of Borcherds forms in a limiting case which falls out the range of applications.
