论文标题
计数与符号晶格和有限集有关的计数函数的中心限制定理
A Central Limit Theorem for Counting Functions Related to Symplectic Lattices and Bounded Sets
论文作者
论文摘要
We use a method developed by Björklund and Gorodnik to show a central limit theorem (as $T$ tends to $\infty$) for the counting functions $\# \left( Λ\cap Ω_T \right)$ where $Λ$ ranges over the space $Y_{2d}$ of symplectic lattices in $ \ mathbb {r}^{2d} $（$ d \ geqslant 4 $）。这里$ \ lbraceω__t\ rbrace_t $是$ \ mathbb {r}^{2d} $中某个有界域的家族，可以通过$ \ mathrm {sp}（sp}（2d，\ mathbbbb {r} r} $ \ mathrm {sp}（ssp}（r）中包含的对角线半流的作用，可以通过对角包含的对角度进行缝制。在此过程中，我们在$ y_ {2d} $上获得了一定高度函数的新$ l^p $界限，最初由Schmidt引入。
We use a method developed by Björklund and Gorodnik to show a central limit theorem (as $T$ tends to $\infty$) for the counting functions $\# \left( Λ\cap Ω_T \right)$ where $Λ$ ranges over the space $Y_{2d}$ of symplectic lattices in $\mathbb{R}^{2d}$ ($d \geqslant 4$). Here $\lbrace Ω_T \rbrace_T$ is a certain family of bounded domains in $\mathbb{R}^{2d}$ that can be tessellated by means of the action of a diagonal semigroup contained in $\mathrm{Sp}(2d, \mathbb{R})$. In the process we obtain new $L^p$ bounds on a certain height function on $Y_{2d}$ originally introduced by Schmidt.
