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arXiv 2402.047842024-02-07math.DSmath.NT

Hecke三角群的尖点等分布

Equidistribution of cusp points of Hecke triangle groups

Laura Breitkopf, Marc Kesseböhmer, Anke Pohl

备注：: 29 pages, 2 figures

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AI总结：

本文在无限遍历理论框架下，利用转移算子技术，将模群尖点等分布结果推广至Hecke三角群，推导了恒定词长群元素编码的加权尖点序列的等分布性质。

摘要：

在无限遍历理论的框架下，我们推导了Hecke三角群尖点的适当加权序列的等分布结果，这些尖点由相对于一组自然生成元具有恒定词长的群元素编码。这是模群相应结果的推广，为此我们依赖于无限遍历理论中的先进结果以及为AFN映射发展的转移算子技术。

英文摘要：

In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural generators. This is a generalization of the corresponding results for the modular group, for which we rely on advanced results from infinite ergodic theory and transfer operator techniques developed for AFN-maps.

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