AI 中文总结
该研究证明了大亏格Weil–Petersson随机闭双曲曲面上，范数在特定区间内的素测地线的归一化加权计数满足渐近高斯分布，拓展了素测地线计数的相关结论。
AI 中文摘要
我们证明，对于亏格很大的Weil–Petersson随机闭双曲曲面，当H≤X且H/log X→∞（X→∞）时，范数在区间(X,X+H]内的素测地线的归一化加权计数渐近高斯分布，特别适用于不一定短的区间。
英文摘要
We show that, for Weil--Petersson random closed hyperbolic surfaces of large genus, the normalized weighted count of prime geodesics with norm in the interval $(X,X+H]$ is asymptotically Gaussian, provided $H \leq X$ and $H/\log X\to\infty$ as $X\to\infty$. In particular, it applies to intervals which are not necessarily short.
Comments8 pages
