Numerical calculation of three-point branched covers of the projective line

Abstract

We exhibit a numerical method to compute three-point branched covers of the complex projective line. We develop algorithms for working explicitly with Fuchsian triangle groups and their finite index subgroups, and we use these algorithms to compute power series expansions of modular forms on these groups.

58 pages, 24 figures; referee's comments incorporated

References in corpus (4)

• Computation of Galois groups of rational polynomials
• Polynomial bounds for Arakelov invariants of Belyi curves
• On computing Belyi maps
• Algorithmic construction of Hurwitz maps

Cited by in corpus (5)

• Gauge Theories and Dessins d'Enfants: Beyond the Torus
• On computing Belyi maps
• A Database of Belyi Maps
• KPZ fluctuations in finite volume
• An approach for computing families of multi-branch-point covers and applications for symplectic Galois groups