Abstract Let G be a finitely generated Fuchsian group of the first kind and let (g : m1, m2, …, mn) be its shortened signature. Beardon showed that almost every Dirichlet region for G has 12g + 4n − 6 sides. Points in ℍ corresponding to Dirichlet regions for G with fewer sides are called exceptional for G. We generalize previously established methods to show that, for any such G, its set of exceptional points is uncountable.

中文翻译：

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第一类有限生成 Fuchsian 群的异常点

摘要 令 G 为第一类有限生成 Fuchsian 群，令 (g : m1, m2, …, mn) 为其缩短签名。Beardon 证明 G 的几乎每个 Dirichlet 区域都有 12g + 4n − 6 边。ℍ 中对应于具有较少边的 G 的狄利克雷区域的点称为 G 的异常点。我们概括先前建立的方法以表明，对于任何这样的 G，其异常点集是不可数的。