Belyi map verification using certified path tracking

Alexandre Guillemot; John Voight

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arXiv · 2604.15562

Belyi map verification using certified path tracking

Alexandre Guillemot·John Voight

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Abstract

We provide an end-to-end workflow to rigorously compute the monodromy of Belyi maps from exact equations over number fields using certified homotopy continuation. We then apply this method at scale to certify the monodromy triples of Belyi maps in the $L$-functions and Modular Forms Database (LMFDB).

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Alexandre Guillemot, John Voight. 2026-04-16. Belyi map verification using certified path tracking. https://arxiv.org/abs/2604.15562

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