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arXiv · 2203.08593

Triangular modular curves of low genus

Juanita Duque-Rosero·John Voight
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Abstract

Triangular modular curves are a generalization of modular curves that arise from quotients of the upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves also arise naturally as a source of Belyi maps with monodromy $\text{PGL}_2(\mathbb{F}_q)$ or $\text{PSL}_2(\mathbb{F}_q)$. We present a computational approach to enumerate Borel-type triangular modular curves of low genus, and we carry out this enumeration for prime level and small genus.

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Juanita Duque-Rosero, John Voight. 2022-03-16. Triangular modular curves of low genus. https://arxiv.org/abs/2203.08593

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