Elliptic Curves: Function Theory, Geometry, Arithmetic

ISBN-13: 9780521658171 / Angielski / Miękka / 1999 / 298 str.

Henry McKean; Victor Moll; Victor Moll

Opis

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.

Recenzje

'With an easy mind the reviewer can recommend this book to those who want to become acquainted with the subject and to those who look for a book which can serve as guide for a course on the subject … the exemplary way in which Elliptic Curves is written, made reviewing a pleasure.' Niew Archief voor Wiskunde

Spis treści

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.