The Research for Eisenstein series and applications

我们的研究有两个主要的结果；一个是几何应用，另一个是与西格尔-韦尔公式的关系。对于几何应用，我们计算了权值g+1和阶数g的Siegel-Eisenstein级数的常数项，这使我们能够计算模变体的一部分上同调。在Siege-Weil公式上，我们可以证明，2阶、权值2、阶数p（素数）的Siegel-Eisenstein级数与格级数重合，而格级数是级数的平均值。该结果是低权重西格尔-韦尔公式的重要例子。

There are two main result in our research ; one is the geometric application, and the other is the relationship to Siegel-Weil formula. For the geometric application, we calculate the constant term of the Siegel-Eisenstein series of weight g+1 and degree g, which allows us to calculate a part of the cohomology of the modular varieties. On Siege-Weil formula, we can show that the Siegel-Eisenstein series of degree 2, weight 2, and level p (prime) coincide with the genus theta series, which is the average of the theta series. Such result is the important example of the Siegel-Weil formula for low weights.