论文标题
Eisenstein系列的零维Shimura品种和中央衍生物
Zero-dimensional Shimura varieties and central derivatives of Eisenstein series
论文作者
论文摘要
我们为（零维）shimura品种的算术siegel-weil公式制定并证明了一个配备了一些其他数据的（零维）的shimura品种。更确切地说，我们定义了一个``特殊的''家族在阿基米德人和非安置的地方的绿色功能方面，证明它们的学位与艾森斯坦系列的中央衍生品的傅立叶系数相吻合一致。证明与平常的概念之间的概念相关。文献中的先前结果。
We formulate and prove a version of the arithmetic Siegel-Weil formula for (zero dimensional) Shimura varieties attached to tori, equipped with some additional data. More precisely, we define a family of ``special" divisors in terms of Green functions at archimedean and non-archimedean places, and prove that their degrees coincide with the Fourier coefficients of the central derivative of an Eisenstein series. The proof relies on the usual Siegel-Weil formula to provide a direct link between both sides of the identity, and in some sense, offers a more conceptual point of view on prior results in the literature.
