Elliptic Curves
Function Theory, Geometry, Arithmetic

Reissued with a new Foreword, this classic work introduces elliptic curves, following in the footsteps of the original discoverers.

Henry McKean (Author), Victor Moll (Author), Alex Kasman (Foreword by)

9781009602112, Cambridge University Press

Paperback / softback, published 6 March 2025

314 pages
22.8 x 15 x 1.7 cm, 0.47 kg

'The book being reviewed is a wonderful text on the subject along an historical path … There is much to learn on almost every page but, to make a proper study of the text, a serious effort has to be made to tackle the exercises, which form an important and integral part of the topic under discussion. There are over 300 items in the references, together with an adequate index, so that the book is also an invaluable text for reference.' Peter Shiu, The Mathematical Gazette

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.

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.

Subject Areas: Geometry [PBM]