论文标题
关于Hecke组对二次字段子集的作用的注释
A note on the action of Hecke groups on subsets of quadratic fields
论文作者
论文摘要
我们研究了线性分数变换产生的组$ h（λ）$的动作q^*（\ sqrt {n}）= \ {\ frac {a+\ sqrt n} {c} {c} \; | \; | \; a，b = \ frac {a^2-n} {c}，c \ in \ mathbb z \ \} $，其中$ n $是$ n $ as a $ n $ s square-free ins square-free ins square-free integer。我们证明，当且仅当$λ= 1 $或$λ= 2 $时，此操作具有有限数量的轨道，并且我们为$λ= 2 $的轨道数给出了上限。
We study the action of the groups $H(λ)$ generated by the linear fractional transformations $x:z\mapsto -\frac{1}{z} \text{ and }w:z\mapsto z+λ$, where $λ$ is a positive integer, on the subsets $\mathbb Q^*(\sqrt{n})=\{\frac{a+\sqrt n}{c}\;|\;a,b=\frac{a^2-n}{c},c\in\mathbb Z\}$, where $n$ is a square-free integer. We prove that this action has a finite number of orbits if and only if $λ=1$ or $λ=2$, and we give an upper bound for the number of orbits for $λ=2$.
