论文标题
$（\ mathrm {sl}（2，\ mathbb {r}）/γ_0）的稀疏等级结果^n $
A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/Γ_0)^n$
论文作者
论文摘要
令$ g = \ mathrm {sl}（2，\ mathbb {r}）^n $，让$γ=γ_0^n $，其中$γ_0$是$ \ mathrm {Slrm {sl}的共同晶格（2，2，\ mathb {r} $，让$ f（让$ f（mathit as a） $ u（x_1，...，x_n）$表示$ g $中的单位元素，该元素生成标准$ n $ dimensional horosphical子组，由$ 2 \ times 2 $上三角矩阵组成。我们证明，在G/γ$中没有任何$ f $的本地障碍物的情况下，稀疏的子集$ \ { 481 $，独立于$γ_0$的光谱差距。
Let $G=\mathrm{SL}(2,\mathbb{R})^n$, let $Γ=Γ_0^n$, where $Γ_0$ is a co-compact lattice in $\mathrm{SL}(2,\mathbb{R})$, let $F(\mathbf{x})$ be a non-singular quadratic form and let $u(x_1,...,x_n)$ denote the unipotent elements in $G$ which generate the standard $n$ dimensional horospherical subgroup, consisting of $2\times 2$ upper triangular unipotent matrices in each co-ordinate. We prove that in absence of any local obstructions for $F$, given any $x_0\in G/Γ$, the sparse subset $\{u(\mathbf{x})x_0:\in\mathbb{Z}^n, F(\mathbf{x})=0\}$ equidistributes in $G/Γ$ as long as $n\geq 481$, independent of the spectral gap of $Γ_0$.
