Regular dessins d'enfants with field of moduli Q(p√2)

Ruben A. Hidalgo, Saul Quispe

Abstract


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.


Keywords


Dessins d'enfants, Riemann surfaces, field of moduli and field of definition

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications