Arithmetic Fuchsian Groups of Genus Zero

Arithmetic Fuchsian Groups of Genus Zero
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零属算术 Fuchsian 群

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发表时间：
2006
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通讯作者：
A. Reid
A. Reid
中科院分区：
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文献类型：
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作者：
D. Long;C. Maclachlan;A. Reid

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如果I是作用在H2上的Flnite余面积Fuchsian群，则商H2=I是一个双曲2-orbilold，其下层空间是一个可定向曲面(可能有穿孔)和若干个Flnite锥点.算术Fuchsian群通过与数论和自同构型理论的密切联系，形成了一个被广泛研究的有趣的Flnite余面积Fuchsian群的子类。本文讨论了当群H~2=I的下表面为亏格为零的算术富氏群I的分布，简而言之，我们称I为亏格为零。对这些群体进行研究的动机来自许多不同的观点
If i is a flnite co-area Fuchsian group acting on H 2 , then the quotient H 2 =i is a hyperbolic 2-orbifold, with underlying space an orientable surface (possibly with punctures) and a flnite number of cone points. Through their close connections with number theory and the theory of automorphic forms, arithmetic Fuchsian groups form a widely studied and interesting subclass of flnite co-area Fuchsian groups. This paper is concerned with the distribution of arithmetic Fuchsian groups i for which the underlying surface of the orbifold H 2 =i is of genus zero; for short we say i is of genus zero. The motivation for the study of these groups comes from many difierent view