Davenport-Zannier Polynomials and Dessins D'Enfants

Nikolai M. Adrianov, Fedor Pakovich, Alexander K. Zvonkin

The French expression "dessins d'enfants" means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.