论文标题
四边形的求和公式
Summation formulae for quadrics
论文作者
论文摘要
我们证明了在偶数变量中的二二次形式的零基因座的泊松求和公式，而对所涉及功能的支持没有假设。公式中的主要新颖性是所有``边界项''均由常数或与原始四相关相关的较小四边形的总和给出。我们还讨论了与经典问题的链接，即估计偶数形式的解决方案数量均匀数量。为了证明求和公式，我们计算$ \ mathrm {sl} _2（\ Mathbb {a} _F）$的琐事表示的theta提升。如Ginzburg，Rallis和Soudry先前所观察到的那样，这是对位于Metapclectic群体全球Schrödinger代表偶数的矢量空间上的正交组的类似物。
We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved. The key novelty in the formula is that all ``boundary terms'' are given either by constants or sums over smaller quadrics related to the original quadric. We also discuss the link with the classical problem of estimating the number of solutions of a quadratic form in an even number of variables. To prove the summation formula we compute (the Arthur truncated) theta lift of the trivial representation of $\mathrm{SL}_2(\mathbb{A}_F)$. As previously observed by Ginzburg, Rallis, and Soudry, this is an analogue for orthogonal groups on vector spaces of even dimension of the global Schrödinger representation of the metaplectic group.
