Herradon has recently provided an example of a regular dessin d’enfant whose field of moduli is the non-abelian extension Q(3√2) answering in this way a question due to Conder, Jones, Streit and Wolfart. In this paper we observe that Herradon’s example belongs naturally to an infinite series of such kind of examples; for each prime integer p ≥ 3 we construct a regular dessin d’enfant whose field of moduli is the non-abelian extension Q(p√2); for p = 3 it coincides with Herradon’s example.
@article{1202,
title = {Regular dessins d'enfants with field of moduli Q(p$\surd$2)},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {14},
year = {2017},
doi = {10.26493/1855-3974.1202.9c1},
language = {EN},
url = {http://dml.mathdoc.fr/item/1202}
}
Hidalgo, Ruben A.; Quispe, Saul. Regular dessins d'enfants with field of moduli Q(p√2). ARS MATHEMATICA CONTEMPORANEA, Tome 14 (2017) . doi : 10.26493/1855-3974.1202.9c1. http://gdmltest.u-ga.fr/item/1202/