Number Theory Seminar

A classical and beautiful result of Gross-Keating relates the intersection of three Hecke correspondences on the integral model of $X_0(1)\times X_0(1)$ with derivative of certain Eisenstein series. Such result can be regarded as an example of arithmetic Siegel-Weil formula and can serve as an ingredient for an arithmetic Gan-Gross-Prasad formula. In this talk, we consider a variant of this formula for the self-product of $X_0(N)$ where $N$ is square-free and  the self-product of Shimura curves respectively. Moreover, we explain how these results confirm a general conjecture for GSpin Shimura varieties with vertex levels. This is joint work with Baiqing Zhu.