**Translations of Mathematical Monographs**

1997;
185 pp;
Hardcover

MSC: Primary 11; 14; 33;

Print ISBN: 978-0-8218-0587-9

Product Code: MMONO/170

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

**Electronic ISBN: 978-1-4704-4585-0
Product Code: MMONO/170.E**

List Price: $103.00

AMS Member Price: $82.40

MAA Member Price: $92.70

# Elliptic Functions and Elliptic Integrals

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*Viktor Prasolov; Yuri Solovyev*

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.

#### Readership

Undergraduate students, graduate students, research mathematicians and physicists interested in elliptic functions.

#### Reviews & Endorsements

A wonderful choice of topics, delivered in a concrete and lively style … provide a lively introduction to many classical topics that lie at the foundations of contemporary algebra, number theory and algebraic geometry.

-- Mathematical Reviews

The strong point of [this] book is the intertwining of complex analysis with algebraic geometry. The book is in fact an elementary introduction to the arithmetic of elliptic curves as well as a treatment of the theory of elliptic functions. the ideal book for a reading course!

-- Mathematische Semesterberichte

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 MATH

#### Table of Contents

# Table of Contents

## Elliptic Functions and Elliptic Integrals

- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Geometry of cubic curves 112
- Elliptic functions 2536
- Arcs of curves and elliptic integrals 5364
- Abel’s theorem on division of lemniscate 6778
- Arithmetic of cubic curves 103114
- Algebraic equations 131142
- Theta functions and solutions of quintic equations 149160
- Bibliography 179190
- Index 183194
- Back Cover Back Cover1198