很多重要数论、算术几何问题与模形式密切相关。Kudla发现一类Eisenstein级数的导数等于以算术cycle为系数的生成函数，也就是著名的算术Siegel-Weil公式。它可以看作是经典Siegel-Weil公式关于Eisenstein级数导数的推广。. 在level平凡的情形下，Kudla,Tonghai等人发现Shimura曲线上存在算术Siegel-Weil公式。本计划主要是证明Shimura曲线上更一般的算术Siegel-Weil公式。这项工作由两部分组成：一是计算一般的Heegner除子和带度量的线丛的交；二是比较它与Eisenstein级数的系数。这项工作不仅能促进算术Siegel-Weil公式以及Kudla program的研究，而且能够丰富Arakelov几何在数论中的应用。

Many important number theory, arithmetic geometry problems are closely related to modular forms. Kudla observed that a fmaily of identites relating the derivates of certain Siegel-Eisenstein series and generating functions for the arithmetic cycles on moduli schemes for abelian variety, which is the famous arithmetic Siegel-Weil formula. It can be thought of generalization of derivatives of classical Siegel-Weil formula on Eisenstein series.. When the level is trivial, Kudla, Tonghai proved an arithmetic formula Siegel-Weil on Shimura curves. We plan to prove more general formula on Shimura curves.The main work of this program are two parts: one is calculating the arithematical intersection of Heegner divisor and metric line bundle, the other is comparing it with coefficients of the Eisenstein series.This work not only can promote the study of arithmetic Siegel-Weil formula and Kudla program, but also enrich the Arakelov geometry applications in number theory.