Elliptic Curves: Function Theory, Geometry, Arithmetic

by Henry McKean, Victor Moll

Overview

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, whose masters were Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows a historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics.

Product Details

ISBN-13:	9780521658171
Publisher:	Cambridge University Press
Publication date:	08/13/1999
Edition description:	New Edition
Pages:	298
Product dimensions:	5.91(w) x 8.94(h) x 0.67(d)

Table of Contents

1. First ideas: complex manifolds, Riemann surfaces, and projective curves; 2. Elliptic functions and elliptic integrals; 3. Theta functions; 4. Modular groups and molecular functions; 5. Ikosaeder and the quintic; 6. Imaginary quadratic fields; 7. The arithmetic of elliptic fields.

Editorial Reviews

"...undergraduates will find that McKean and Moll's book...offers more diverse viewpoints [than other books on elliptic curves]. Highly recommended."
Choice

"...this is a wonderful book that should reward those who have the background for it with immense joy and insight."
SIAM Review

From the Publisher