论文标题
三角形模块曲线的收缩长度
Systolic length of triangular modular curves
论文作者
论文摘要
我们提出了一种计算上限的方法，以通过双曲三角形组的一致性亚组统一的某些Riemann表面的收缩期长度，并承认一致性Hurwitz曲线是一种特殊情况。统一的组被实现为紫红色组，并计算出方便的有限生成集。上限源自发电机的痕迹。给出了一些明确的计算，包括用于非弧度表面的计算。我们应用COSAC和Dória的结果表明，相对于该属，收缩期长度在对数上生长。
We present a method for computing upper bounds on the systolic length of certain Riemann surfaces uniformized by congruence subgroups of hyperbolic triangle groups, admitting congruence Hurwitz curves as a special case. The uniformizing group is realized as a Fuchsian group and a convenient finite generating set is computed. The upper bound is derived from the traces of the generators. Some explicit computations, including ones for non-arithmetic surfaces, are given. We apply a result of Cosac and Dória to show that the systolic length grows logarithmically with respect to the genus.
