论文标题
Eisenstein系列和Kudla-Millson Theta Lift的对角线限制
Diagonal restriction of Eisenstein series and Kudla-Millson theta lift
论文作者
论文摘要
我们考虑了与签名$（n，n）$相关的二次空间相关的Kudla-Millson Theta系列。通过将“远见”论点与siegel-weil公式相结合，我们表明其（正则化）沿着与完全真实的$ n $的圆环不可或缺的积分是Eisenstein系列的对角线限制。它使我们能够将对角线限制的傅立叶系数表示为相交数字，这将达尔蒙pozzi-vonk的结果推广到完全真实的领域。
We consider the Kudla-Millson theta series associated to a quadratic space of signature $(N,N)$. By combining a `see-saw' argument with the Siegel-Weil formula, we show that its (regularized) integral along a torus attached to a totally real field of degree $N$ is the diagonal restriction of an Eisenstein series. It allows us to express the Fourier coefficients of the diagonal restriction as intersection numbers, which generalizes a result of Darmon-Pozzi-Vonk to totally real fields.
