Davenport–Zannier Polynomials and Dessins d’Enfants

Download or read book Davenport–Zannier Polynomials and Dessins d’Enfants written by Nikolai M. Adrianov and published by American Mathematical Soc.. This book was released on 2020-06-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The major part of the book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics. The reader may either take the basic facts of these theories for granted or use our book as a motivation and a first approach to these subjects.