A three-parameter clan of Hurwitz–Belyi maps
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2018), pp. 69-83.

We study a collection of Hurwitz–Belyi maps depending on three integer parameters, finding formulas uniform in the parameters.

Nous étudions une certaine collection d’applications d’Hurwitz–Belyi dépendant de trois paramètres avec l’obtention de formules uniformes.

Published online:
DOI: 10.5802/pmb.22
Classification: 14H57,  33E99
Keywords: Belyi map, discriminant, monodromy
David P. Roberts 1

1 Division of Science and Mathematics, University of Minnesota Morris, Morris, Minnesota, 56267, USA
@article{PMB_2018____69_0,
     author = {David P. Roberts},
     title = {A three-parameter clan of {Hurwitz{\textendash}Belyi} maps},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
     pages = {69--83},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2018},
     doi = {10.5802/pmb.22},
     language = {en},
     url = {https://pmb.centre-mersenne.org/articles/10.5802/pmb.22/}
}
TY  - JOUR
TI  - A three-parameter clan of Hurwitz–Belyi maps
JO  - Publications mathématiques de Besançon. Algèbre et théorie des nombres
PY  - 2018
DA  - 2018///
SP  - 69
EP  - 83
PB  - Presses universitaires de Franche-Comté
UR  - https://pmb.centre-mersenne.org/articles/10.5802/pmb.22/
UR  - https://doi.org/10.5802/pmb.22
DO  - 10.5802/pmb.22
LA  - en
ID  - PMB_2018____69_0
ER  - 
%0 Journal Article
%T A three-parameter clan of Hurwitz–Belyi maps
%J Publications mathématiques de Besançon. Algèbre et théorie des nombres
%D 2018
%P 69-83
%I Presses universitaires de Franche-Comté
%U https://doi.org/10.5802/pmb.22
%R 10.5802/pmb.22
%G en
%F PMB_2018____69_0
David P. Roberts. A three-parameter clan of Hurwitz–Belyi maps. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2018), pp. 69-83. doi : 10.5802/pmb.22. https://pmb.centre-mersenne.org/articles/10.5802/pmb.22/

[1] Jean-Marc Couveignes Quelques revêtements définis sur , Manuscr. Math., Volume 92 (1997) no. 4, pp. 409-445 | Article | MR: 1441485 | Zbl: 0946.14015

[2] Robert Guralnick; Kay Magaard On the minimal degree of a primitive permutation group, J. Algebra, Volume 207 (1998) no. 1, pp. 127-145 | Article | MR: 1643074 | Zbl: 0911.20003

[3] Gunter Malle; David P. Roberts Number fields with discriminant ±2 a 3 b and Galois group A n or S n , LMS J. Comput. Math., Volume 8 (2005), p. 80-101 (electronic) | Article | MR: 2135031 | Zbl: 1119.11064

[4] Fedor Pakovich; Alexander K. Zvonkin Minimum degree of the difference of two polynomials over , and weighted plane trees, Selecta Math. (N.S.), Volume 20 (2014) no. 4, pp. 1003-1065 | Article | MR: 3273629 | Zbl: 1316.11057

[5] Fedor Pakovich; Alexander K. Zvonkin Minimum degree of the difference of two polynomials over , Part II: Davenport-Zannier pairs (2015) (https://arxiv.org/abs/1509.07973)

[6] David P. Roberts Hurwitz-Belyi maps, Publ. Math. Besançon, Algèbre Théorie Nombres, Volume 6 (2018), pp. 25-67

Cited by Sources: