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arXiv · 2012.08796

Systolic length of triangular modular curves

Michael M. Schein·Amir Shoan
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Abstract

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 D\'{o}ria to show that the systolic length grows logarithmically with respect to the genus.

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Michael M. Schein, Amir Shoan. 2020-12-16. Systolic length of triangular modular curves. https://arxiv.org/abs/2012.08796

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