On the ring structure of automorphic forms and differential operators

我们在这个项目上的目的是利用微分算子来确定自同构形的结构。在这两年中，我们得到了以下两个结果：(1)关于具有小判别式的实二次域的Hilbert模形式的结构，我们得到了当权差较小时的结构定理；(2)关于向量值二次Siegel模形式的结构，当离散子群是小水平同余子群时，我们得到了一个结构定理。

Our aim on this project is to determine the structure of automorphic forms by using differential operators. In this two years, we have the following two results :(1) On the structure of Hilbert modular forms with respect to a real quadratic field with small discriminant, we have a structure theorem when the difference of the weight is small.(2) On the structure of vector valued Siegel modular forms of degree 2, we have a structure theorem when the discrete subgroup is in a congruent subgroup with a small level.