Elliptic Curves

Function Theory, Geometry, Arithmetic

Henry McKean (New York University), Victor Moll (Tulane University, Louisiana), Alex Kasman (College of Charleston, South Carolina)

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English

Cambridge University Press
06 March 2025

Geometry

Series: Cambridge Mathematical Library

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more 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 an 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. 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, with many exercises with hints scattered throughout the text.

By: Henry McKean (New York University), Victor Moll (Tulane University, Louisiana)
Foreword by: Alex Kasman (College of Charleston South Carolina)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
ISBN: 9781009602112
ISBN 10: 100960211X
Series: Cambridge Mathematical Library
Pages: 310
Publication Date: 06 March 2025
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Forthcoming

Foreword: Preface; 1. First ideas: complex manifolds, Riemann surfaces, and projective curves; 2. Elliptic integrals and functions; 3. Theta functions; 4. Modular groups and modular functions; 5. Ikosaeder and the quintic; 6. Imaginary quadratic number fields; 7. Arithmetic of elliptic curves; References; Index.