论文标题
霍斯术等级的抽象光谱方法
An abstract spectral approach to horospherical equidistribution
论文作者
论文摘要
本文介绍了一种抽象的光谱方法，以证明双曲线歧管中扩展的hhosphers的有效等分。该方法是由（Lax-Phillips 1982）开发的计算方法所激发的，该方法产生了高效，明确的错误术语。为了展示这种方法的灵活性，我们证明了在$ t^1（\ Mathbb {h}^{n+1}）$中的有效halospherical等分定理，并且在较高的等级设置中，$ \ operatotorName {sl} _n（sl} _n（\ mathbb {r}）
This paper introduces an abstract spectral approach to prove effective equidistribution of expanding horospheres in hyperbolic manifolds. The method, which is motivated by the approach to counting developed by (Lax-Phillips 1982), produces highly effective, explicit error terms. To exhibit the flexibility of this method we prove effective horospherical equidistribution theorems in $T^1(\mathbb{H}^{n+1})$ and in the higher rank setting, $\operatorname{SL}_n(\mathbb{R})/\operatorname{SO}_n(\mathbb{R})$.
