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Elliptic Functions and Elliptic Integrals
Viktor Prasolov, Independent University of Moscow, Russia, and Yuri Solovyev, Moscow State University, Russia

Translations of Mathematical Monographs
1997; 185 pp; hardcover
Volume: 170
ISBN-10: 0-8218-0587-8
ISBN-13: 978-0-8218-0587-9
List Price: US$103
Member Price: US$82.40
Order Code: MMONO/170
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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.


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


"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

  • Geometry of cubic curves
  • Elliptic functions
  • Arcs of curves and elliptic integrals
  • Abel's theorem on division of lemniscate
  • Algebraic equations
  • Theta functions and solutions of quintic equations
  • Bibliography
  • Index
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