论文标题
prime
Windings of prime geodesics
论文作者
论文摘要
模块化Orbifold周围的封闭导向的大地测量的绕组是由Rademacher符号计算得出的，Rademacher符号是从模块化形式理论中的经典函数。在本文中，我们介绍了缠绕数字的新结构，以记录有关封闭的封闭的大地测量学，内容涉及一般垂直的双曲线孔的规定尖端。对于各种表面的算术家族，该缠绕数可以通过rademacher符号再次表达，并且访问自动形式的光谱理论可产生统计结果，这些结果就其绕组而言的封闭（原始）定向的大地测量学的分布产生了统计结果。
The winding of a closed oriented geodesic around the cusp of the modular orbifold is computed by the Rademacher symbol, a classical function from the theory of modular forms. In this article, we introduce a new construction of winding numbers to record the winding of closed oriented geodesics about a prescribed cusp of a general cusped hyperbolic orbifold. For various arithmetic families of surfaces, this winding number can again be expressed by a Rademacher symbol, and access to the spectral theory of automorphic forms yields statistical results on the distribution of closed (primitive) oriented geodesics with respect to their winding.
