论文标题
Selberg的$ 3/16 $定理的概括，用于COCOCOCOCOCKACT薄型子组的$ \ permatatorName {so}（so}（n，1）$
Generalization of Selberg's $3/16$ theorem for convex cocompact thin subgroups of $\operatorname{SO}(n, 1)$
论文作者
论文摘要
令$γ$为$ \ operatatorName {so}（n，1）$的算术晶格的凸Cocompact薄亚组。我们将Selberg的$ \ frac {3} {16} $定理在此设置中，即，我们证明了框架流的统一指数混合，并获得了均匀的共振半平面，以覆盖均匀的一半平面，以覆盖双重歧管$γ\ backslash \ backslash \ backslash \ mathbb h^n $。这扩展了建立$ n = 2 $案例的OH Winter的工作。该定理从均匀的光谱范围遵循具有载体的一致性转移运算符。我们在一致性涵盖的范围内统一地采用了Sarkar-Winter的框架流程版，以及Golsefidy-varjú通过使用返回轨迹子组的属性和trace trage traightory子组的属性是zariski deense and the proge fields conconceccicciccy $γ。这些属性是通过证明返回轨迹子组在$γ$中的有限指数。
Let $Γ$ be a convex cocompact thin subgroup of an arithmetic lattice in $\operatorname{SO}(n, 1)$. We generalize Selberg's $\frac{3}{16}$ theorem in this setting, i.e., we prove uniform exponential mixing of the frame flow and obtain a uniform resonance-free half plane for the congruence covers of the hyperbolic manifold $Γ\backslash \mathbb H^n$. This extends the work of Oh-Winter who established the $n = 2$ case. The theorem follows from uniform spectral bounds for the congruence transfer operators with holonomy. We employ Sarkar-Winter's frame flow version of Dolgopyat's method uniformly over the congruence covers as well as Golsefidy-Varjú's generalization of Bourgain-Gamburd-Sarnak's expansion machinery by using the properties that the return trajectory subgroups are Zariski dense and have trace fields which coincide with that of $Γ$. These properties follow by proving that the return trajectory subgroups have finite index in $Γ$.
