Elliptic Functions and Elliptic Integrals

✍ Scribed by Viktor Prasolov and Yuri Solovyev

• Publisher: American Mathematical Society
• Year: 1997
• Tongue: English
• Leaves: 191
• Series: Translations of Mathematical Monographs 170
• Category: Library

✦ Synopsis

This book take a curious and rather unconventionnal path to elliptic fonctions and integrals. Instead of dealing with sn, cn dn and so on, it takes from the begining a gemotrical approach: the first chapter is devoted to cubic curves and various theorem on addition of points on them. The second chapter introduces the weierstrass p(z) functions as an explicit construction of an elliptic function and use that to parametrize the cubic curves. Chapter 3 deals with elliptic integrals at length.These 3 chapters are the core of the book. The next chapters deal with more advanced subjects such as arithmetic of cubic curves and division of lemniscate. The end of the book is devoted to the solution of algebraic equations, and the use of theta function for the resolution of quintic. For anybody interested in elliptic functions, the first 3 chapters are elegant and necessitate only a small background in complex variable analysis. I don't see the coherence between the other chapters. There are mainly dissertations on some nice topics.