On the Belyi degree of a number field
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
In this short note we introduce the Belyi degree of a number field K, which is the smallest degree of a dessin d'enfant having K as field of moduli. After the description of some general properties (for example, the fact that there exist finitely many number fields of bounded Belyi degree), we give a lower and an upper bound for such an invariant. We finally give some explicit examples for quadratic fields.
Cite
@article{arxiv.math/0611135,
title = {On the Belyi degree of a number field},
author = {Leonardo Zapponi},
journal= {arXiv preprint arXiv:math/0611135},
year = {2007}
}