论文标题
Hejhal算法扩展到无限量基本域
An Extension of Hejhal's Algorithm to Infinite Volume Fundamental Domains
论文作者
论文摘要
这项工作提出了一种用于计算Maass形式的算法及其特征值，用于Fuchsian Infinite Covolume组。通过帕特森 - 苏利文理论，这具有计算这些组极限集的Hausdorff维度的额外好处。为了近似Maass形式，我们考虑了它们在不同坐标系中的傅立叶扩展。为了处理无限的体积基本域，我们利用了火炬域的概念。我们还开发了有关耀斑领域中傅立叶扩展的理论，这些理论模仿了有关尖口扩展的经典理论。最后，我们介绍了应用于对称的Schottky组和无限体积Hecke组的算法的详细示例。
This work presents an algorithm for numerically computing Maass forms and their eigenvalues for Fuchsian groups of infinite covolume. By Patterson-Sullivan theory, this has the added benefit of computing Hausdorff dimensions of the limit sets of these groups. To approximate Maass forms, we consider their Fourier expansions in different coordinate systems. To handle infinite volume fundamental domains, we make use of the concept of flare domains. We also develop theory about Fourier expansions in flare domains which mimics the classical theory on expansions with respect to cusps. Finally, we present detailed examples of the algorithm applied to symmetric Schottky groups and infinite volume Hecke groups.
