论文标题
在二曲线二曲歧管的长度上
On Length Sets of Subarithmetic Hyperbolic Manifolds
论文作者
论文摘要
我们在双曲线歧管上的长度集上制定了渐近长度饱和的猜想，其基本组是亚取m的，即包含在算术组中。我们证明了刺穿的Zariski致密盖的猜想的第一个实例。所涉及的工具包括轨道圆法，膨胀和计数薄型组的一致性，指数总和的估计，双线性形式和二次L系列。
We formulate the Asymptotic Length-Saturation Conjecture on the length sets of closed geodesics on hyperbolic manifolds whose fundamental groups are subarithmetic, that is, contained in an arithmetic group. We prove the first instance of the conjecture for punctured, Zariski dense covers of the modular surface. The tools involved include the Orbital Circle Method, expansion and counting in congruence towers of thin groups, estimates for exponential sums, bilinear forms, and quadratic L-series.
