论文标题
Sato主题的变化
Variations on themes of Sato
论文作者
论文摘要
在本文的第一部分中，我们回顾了与球形还原前均匀矢量空间相关的局部Zeta积分的形式主义，该空间通过结合了可允许表示的广义矩阵系数，部分地扩展了M. Sato的理论。我们总结了这些积分的基本属性，例如收敛，杂形延续和抽象功能方程。在第二部分中，我们证明了适合某些非球形空间的概括。作为一种应用，由此产生的理论适用于巴尔加瓦的立方体的固定前载体空间，这也被F. sato和Suzuki-Wakatsuki考虑在其对复曲面时期的研究中。
In the first part of this article, we review a formalism of local zeta integrals attached to spherical reductive prehomogeneous vector spaces, which partially extends M. Sato's theory by incorporating the generalized matrix coefficients of admissible representations. We summarize the basic properties of these integrals such as the convergence, meromorphic continuation and an abstract functional equation. In the second part, we prove a generalization that accommodates certain non-spherical spaces. As an application, the resulting theory applies to the prehomogeneous vector space underlying Bhargava's cubes, which is also considered by F. Sato and Suzuki-Wakatsuki in their study of toric periods.
