On computing Belyi maps

J. Sijsling[1]; J. Voight[2]

  • [1] Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK
  • [2] Department of Mathematics and Statistics, University of Vermont, 16 Colchester Ave, Burlington, VT 05401, USA; Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA

Publications mathématiques de Besançon (2014)

  • Issue: 1, page 73-131
  • ISSN: 1958-7236


We survey methods to compute three-point branched covers of the projective line, also known as Belyĭ 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.

How to cite


Sijsling, J., and Voight, J.. "On computing Belyi maps." Publications mathématiques de Besançon (2014): 73-131. <http://eudml.org/doc/275717>.

abstract = {We survey methods to compute three-point branched covers of the projective line, also known as Belyĭ 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.},
affiliation = {Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK; Department of Mathematics and Statistics, University of Vermont, 16 Colchester Ave, Burlington, VT 05401, USA; Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA},
author = {Sijsling, J., Voight, J.},
journal = {Publications mathématiques de Besançon},
keywords = {Belyi maps; dessins d’enfants; covers; uniformization; computational algebra; dessins d'enfants},
language = {eng},
number = {1},
pages = {73-131},
publisher = {Presses universitaires de Franche-Comté},
title = {On computing Belyi maps},
url = {http://eudml.org/doc/275717},
year = {2014},

AU - Sijsling, J.
AU - Voight, J.
TI - On computing Belyi maps
JO - Publications mathématiques de Besançon
PY - 2014
PB - Presses universitaires de Franche-Comté
IS - 1
SP - 73
EP - 131
AB - We survey methods to compute three-point branched covers of the projective line, also known as Belyĭ 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.
LA - eng
KW - Belyi maps; dessins d’enfants; covers; uniformization; computational algebra; dessins d'enfants
UR - http://eudml.org/doc/275717
ER -


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