论文标题
Selberg Zeta功能的零，用于对称无限面积双曲线表面
Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces
论文作者
论文摘要
在本文中，我们为某些非常对称的无限面积表面$ x $描述了Selberg Zeta函数的零零$ z_x $的简单数学基础。为了确定，我们考虑了三个漏斗表面的情况。我们表明Zeta函数是一个复杂的几乎周期函数，可以通过大域上的复杂三角多项式（在定理4.2）上近似。作为我们的主要应用程序，我们就Borthwick（Arxiv：1305.4850）（在定理1.5中）的惊人经验结果提供了解释，该结果就标准曲线$ \ MATHCAL C $ C $ conterged缩放的零集的收敛性而言。
In the present paper we give a simple mathematical foundation for describing the zeros of the Selberg zeta functions $Z_X$ for certain very symmetric infinite area surfaces $X$. For definiteness, we consider the case of three funneled surfaces. We show that the zeta function is a complex almost periodic function which can be approximated by complex trigonometric polynomials on large domains (in Theorem 4.2). As our main application, we provide an explanation of the striking empirical results of Borthwick (arXiv:1305.4850) (in Theorem 1.5) in terms of convergence of the affinely scaled zero sets to standard curves $\mathcal C$.
