紧致双曲曲面中闭测地线的尖锐有效等分布
Sharp effective equidistribution of closed geodesics in compact hyperbolic surfaces
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中文总结 AI 辅助
本文通过分析Zelditch迹公式并建立矩阵系数的尖锐上界，证明了紧致双曲曲面上闭测地线的尖锐有效等分布定理。
中文摘要 AI 辅助
我们证明了紧致双曲曲面上闭测地线的尖锐有效等分布定理。这是通过仔细分析由Maass特征函数扭曲的Selberg迹公式（我们称之为Zelditch迹公式）实现的，遵循Zelditch的观察，即几何侧可以表示为闭测地线上特征函数的周期积分之和。主要技术输入是矩阵系数$\langle ϕ, φ^2 \rangle$的尖锐上界，该上界在$t_ϕ\to \infty$和$t_φ\to \infty$时一致成立，其中$t_ϕ$和$t_φ$是对应于$X$上Maass形式$ϕ$和$φ$的特征参数。
英文摘要
We prove a sharp effective equidistribution theorem for closed geodesics on a compact hyperbolic surface. This is achieved by carefully analyzing the Selberg trace formula twisted by a Maass eigenfunction, which we refer to as Zelditch's trace formula, following Zelditch's observation that the geometric side can be expressed as a sum of period integrals of eigenfunctions on closed geodesics. The main technical input is a sharp upper bound for the matrix coefficients $\langle ϕ, φ^2 \rangle$ uniformly in $t_ϕ\to \infty$ and $t_φ\to \infty$, where $t_ϕ$ and $t_φ$ are the eigenparameters corresponding to Maass forms $ϕ$ and $φ$ on $X$.
发表机构
- Brown University（布朗大学）
- Stony Brook University（石溪大学）
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