A substantial part of the theory of dessins d’enfants could have been developed in the 19th century. However, the fundamental theorem that lies at the basis of the theory was established by G. V. Belyi1  only in 1979. Below we formulate the theorem, but postpone its proof until the very end of the chapter (Sec. 2.6). This order of exposition permits the reader to begin by acquiring some experience, by seeing examples and following the accompanying discussion.
KeywordsMeromorphic Function Elliptic Curve Galois Group Chebyshev Polynomial Algebraic Number
Unable to display preview. Download preview PDF.