论文标题
在$ \ mathrm {sl} _2（\ mathbb {r}）/\ mathrm {sl} _2（\ Mathbb {Z}）$上
On an extreme value law for the unipotent flow on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$
论文作者
论文摘要
我们研究了模块表面$ \ mathrm {sl} _2（\ Mathbb {r}）/\ Mathrm {SL} _2（\ Mathbb {Z}）$的单位表面流量的极值分布。使用同质动力学和数字的工具，我们证明存在连续的分布函数$ f（r）$，用于归一化的最深层尖端偏移。我们在[ - \ frac {1} {2} {2} \ log 2，\ infty）$中找到了$ f（r）$ for $ f（r）$的封闭分析公式，并建立$ f（r）$的渐近行为为$ r \ to- \ to- \ infty $。
We study an extreme value distribution for the unipotent flow on the modular surface $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Using tools from homogenous dynamics and geometry of numbers we prove the existence of a continuous distribution function $F(r)$ for the normalized deepest cusp excursions of the unipotent flow. We find closed analytic formulas for $F(r)$ for $r \in [-\frac{1}{2} \log 2, \infty)$, and establish asymptotic behavior of $F(r)$ as $r \to -\infty$.
