论文标题
Siegel的Zeta功能的模块化
The modularity of Siegel's zeta functions
论文作者
论文摘要
Siegel定义了与不确定二次形式相关的ZETA函数，并证明了它们的分析属性，例如分析连续性和功能方程。这些Zeta函数的系数称为表示的度量，并且在二次形式的算术理论中起重要作用。在1938年的一篇论文中，西格尔评论了其Zeta功能的模块化将在合适的匡威定理的帮助下证明其模块化。在本文中，我们通过使用Weil-Type Converse定理来完成Siegel的原始计划，该计划最近出现了。还显示Siegel的Zeta函数的“一半”对应于Holomormormormormormormormormormormormormormormormormorthic形式。
Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of representations, and play an important role in the arithmetic theory of quadratic forms. In a 1938 paper, Siegel made a comment to the effect that the modularity of his zeta functions would be proved with the help of a suitable converse theorem. In the present paper, we accomplish Siegel's original plan by using a Weil-type converse theorem for Maass forms, which has appeared recently. It is also shown that "half" of Siegel's zeta functions correspond to holomorphic modular forms.
