Arithmetic Fuchsian groups with signature $(1; e)$
Arithmetic Fuchsian groups with signature $(1; e)$
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带签名 $(1; e)$ 的算术 Fuchsian 群
DOI：
10.2969/jmsj/03530381
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发表时间：
1983
影响因子：
0.7
通讯作者：
K. Takeuchi
中科院分区：
文献类型：
--
作者：
K. Takeuchi
在文献[17]，[18]中，我们确定了所有算术三角Fuchsian群.本文的目的是确定所有具有签名$（$1; $e）$的算术Fuchsian群。在\S2中，我们证明了对任意非负整数g和t，存在n个具有符号（g;e_{1}，e_{2}，\cdots，e_{t}）$直到SL_{2}（R）$-共轭的算术Fuchsian群（定理2.1）.在\S 3中，我们处理具有签名（1; e）$（即$）的算术Fuchsian群\Gamma$。$g=1$，
In the previous papers [17], [18] we determined all arithmetic triangle Fuchsian groups. The purpose of this paper is to determine all arithmetic Fuchsian groups with signature $($1; $e)$ . In \S 2, we prove that for arbitrary nonnegative integers $g$ and $t$ there exist finitely many arithmetic Fuchsian groups with signature $(g;e_{1}, e_{2}, \cdots , e_{t})$ up to $SL_{2}(R)$-conjugation (Theorem 2.1). In \S 3 we deal with arithmetic Fuchsian groups $\Gamma$ with signature (1; e) $(i.e$ . $g=1$ ,