On computing Belyi maps
Number Theory
2018-11-13 v3 Algebraic Geometry
Complex Variables
Group Theory
Abstract
We survey methods to compute three-point branched covers of the projective line, also known as Belyi maps. These methods include a direct approach, involving the solution of a system of polynomial equations, as well as complex analytic methods, modular forms methods, and p-adic methods. Along the way, we pose several questions and provide numerous examples.
Keywords
Cite
@article{arxiv.1311.2529,
title = {On computing Belyi maps},
author = {Jeroen Sijsling and John Voight},
journal= {arXiv preprint arXiv:1311.2529},
year = {2018}
}
Comments
57 pages, 3 figures, extensive bibliography; English and French abstract; revised according to referee's suggestions