论文标题
Shimura曲线及其周期性的地球持续分数：$（2,3,7）$ - 三角形组的情况
Geodesic continued fraction for Shimura curves and its periodicity: the case of $(2,3,7)$-triangle group
论文作者
论文摘要
在本文中，我们研究了从$（2,3,7）$ - 三角形组的Shimura曲线的情况下，地球持续的分数。我们使用Shimura曲线上的大地测量学编码进行了一定的持续分数扩展，并证明了扩展的Lagrange类型周期定理，该定理定理捕获了$ \ Mathbb {Q}（Q}（Q}（\ cos（cos）（\ cos/2 qout/2oud/7）），$ \ mathbb {Q}（Qous/7）的基本相对单位$ \ cos（qus/7）与一组相对单位。我们还讨论了这些持续分数的融合。
In this paper we study the geodesic continued fraction in the case of the Shimura curve coming from the $(2,3,7)$-triangle group. We construct a certain continued fraction expansion of real numbers using the so-called coding of the geodesics on the Shimura curve, and prove the Lagrange type periodicity theorem for the expansion which captures the fundamental relative units of quadratic extensions of $\mathbb{Q}(\cos(2π/7))$ with rank one relative unit groups. We also discuss the convergence of these continued fractions.
