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.
Bibliographical noteFunding Information:
The first author was supported by the Germany-Israel Foundation for Scientific Research and Development under grant 1246/2014 during part of this work.
© 2021 Elsevier Inc.
- Congruence subgroups
- Quaternion algebras
- Semiarithmetic groups
- Triangle groups