Computation of genus 0 Belyi functions. Belyi functions is a captivating field of research in algebraic geometry, complex analysis, Galois theory. However, computation of Belyi functions of degree over 20 is still considered hard. If the desired branching pattern is nearly regular, pull-back transformations of hypergeometric equations to Fuchsian equations with just a few singularities can be used. This allows computation of Belyi functions of degree 60 and beyond. An implementation in Maple for computing genus 0 Belyi functions will be presented. The implementation is available at rvidunas/ComputeBelyi.mpl.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Ishkhanyan, A. M.: Generalized hypergeometric solutions of the Heun equation (2020)
  2. Vidunas, Raimundas; He, Yang-Hui: Genus one Belyi maps by quadratic correspondences (2020)
  3. van Hoeij, Mark; Kunwar, Vijay Jung: Classifying (almost)-Belyi maps with five exceptional points (2019)
  4. Vidunas, Raimundas: Dihedral evaluations of hypergeometric functions with the Kleinian projective monodromy (2019)
  5. Combot, Thierry: Integrability of the one dimensional Schrödinger equation (2018)
  6. Ishkhanyan, T. A.; Ishkhanyan, A. M.: The third five-parametric hypergeometric quantum-mechanical potential (2018)
  7. Ishkhanyan, T. A.; Shahverdyan, T. A.; Ishkhanyan, A. M.: Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients (2018)
  8. Vidunas, Raimundas; He, Yang-Hui: Composite genus one Belyi maps (2018)
  9. Abdelaziz, Y.; Maillard, J.-M.: Modular forms, Schwarzian conditions, and symmetries of differential equations in physics (2017)
  10. Abdelaziz, Y.; Maillard, J.-M.: Schwarzian conditions for linear differential operators with selected differential Galois groups (2017)
  11. Imamoglu, Erdal; van Hoeij, Mark: Computing hypergeometric solutions of second order linear differential equations using quotients of formal solutions and integral bases (2017)
  12. Shabat, G.: Calculating and drawing Belyi pairs (2017)
  13. van Hoeij, Mark; Vidūnas, Raimundas: Belyi functions for hyperbolic hypergeometric-to-Heun transformations (2015)
  14. van Hoeij, Mark; Vidunas, Raimundas: Computation of genus 0 Belyi functions (2014)