Elliptic Functions and Elliptic Integrals (Translations of Mathematical Monographs) by Viktor Prasolov and Yuri Solovyev (PDF)

Description

This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel’s theorem on the lemniscate and Hermite’s solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.

User’s Reviews

Editorial Reviews: From the Publisher Provides a great panoramic view for the beginner in the field. The style of writing is very cultured, with a sympathetic understanding and respect of the pioneering work of the old masters, and with a delightful sense of aesthetics and beauty. This book really breathes the charm and the fine art of the mathematics of Abel’s era, and it is mainly this particular feature that makes the book under review fairly unique and highly valuable. Experts and teachers can benefit from the reading of this text likewise. Zentralblatt f”ur Mathematik”

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐ok hose

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