Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues,Proceedings of the American Mathematical Society

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Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-09 , DOI: 10.1090/proc/15152
Brian Benson , Grant Lakeland , Holger Then

Abstract:We compute the Cheeger constants of a collection of hyperbolic surfaces corresponding to maximal non-cocompact arithmetic Fuchsian groups, and to subgroups which are the rotation subgroup of maximal reflection groups. The Cheeger constants are geometric quantities, but relate to the smallest eigenvalues of Maass cusp forms. From geometrical considerations, we find evidence for the existence of small eigenvalues. We search for these small eigenvalues and compute the corresponding Maass cusp forms numerically.

中文翻译：

双曲反射群的Cheeger常数和小特征值的Maass尖点形式

摘要：我们计算了与最大非紧致算术Fuchsian组相对应的双曲面集合的Cheeger常数，并且该子集是最大反射组的旋转子组。Cheeger常数是几何量，但与Maass尖点形式的最小特征值有关。从几何方面的考虑，我们发现存在小特征值的证据。我们搜索这些小的特征值，并通过数值计算相应的马斯尖峰形式。

更新日期：2020-11-12

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