论文标题
灯锥的第二刻西格尔变换和应用
Second moment of the light-cone Siegel transform and applications
论文作者
论文摘要
我们研究了灯孔的siegel变换，在合理的非定义二次二次形式的光锥上转换功能，以在同质空间$ \ text {so}^+_ q（\ mathbb {z}）\ backslash \ backslash \ so}^+_ q（so}^+_ q（s s so}^^q（so} Q（s so}））中，特别是，我们证明了此转换的第二瞬间公式，用于签名$（n+1,1）$的形式，并展示如何将其用于各种应用程序，以计算光锥上的整数点。特别是，我们证明了椭圆形的固有双苯胺近似以及光锥上随机线性和二次形式的值的分布。
We study the light-cone Siegel transform, transforming functions on the light cone of a rational indefinite quadratic form $Q$ to a function on the homogenous space $\text{SO}^+_Q(\mathbb{Z})\backslash \text{SO}^+_Q(\mathbb{R})$. In particular, we prove a second moment formula for this transform for forms of signature $(n+1,1)$, and show how it can be used for various applications for counting integer points on the light cone. In particular, we prove some new results on intrinsic Diophantine approximations on ellipsoids as well as on the distribution of values of random linear and quadratic forms on the light cone.
