On the equivalence relations of α-continued fractions
On the equivalence relations of α-continued fractions
复制标题
关于α-连分数的等价关系
DOI：
10.1016/j.indag.2014.02.006
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Rie Natsui
中科院分区：
文献类型：
--
作者：
Hitoshi Nakada;Rie Natsui
本文比较了由最终一致的α-连分式展开（0≤ α≤ 1）与由共享GL（2，Z）-或SL（2，Z）-轨道所产生的真实的数的等价关系。本文证明了当x是无界型时，x的α-关系与GL（2，Z）-关系对任意α> 0是相同的.另一方面，对于有界类型的x，它们不相同。
We compare the equivalence relations on real numbers arising from having eventually agreeing α-continued fraction expansion (for each 0≤ α≤ 1) with those from sharing GL (2, Z)-or SL (2, Z)-orbits. We show that the α-relation and the GL (2, Z)-relation of x are identical for any α> 0 when x is of unbounded type. On the other hand, they are not identical for x of bounded type.