Explicit trace formulas for Hecke operators on spaces of modular forms of several variables

在这项研究中，我们已经明确地计算几何方面的迹公式，以获得具体的数值的Hecke算子的迹空间的Siegel尖点形式的二度。因此，我们得到了每个共轭类在几何方面的贡献的算术公式。应用这些公式，我们得到了空间维数（平凡作用的迹）的显式公式的一些结果，并部分地解决了某些Hecke算子对合的迹的计算问题。

In this study, we have explicitly calculated geometric sides of trace formulas, in order to derive concrete numerical values of traces of Hecke operators on spaces of Siegel cusp forms of degree two. Therefore, we have obtained arithmetic formulas for contributions of each conjugacy classes in the geometric side. Applying the formulas, we got some results on explicit formulas for dimension of spaces(traces of trivial actions) and we partly solved computations for traces of involutions as certain Hecke operators.