Elliptic Curves

Function Theory, Geometry, Arithmetic
Erscheinungsjahr 2011
ISBN: 978-0-521-65817-1
Verlag: Cambridge University Press

Buch, Englisch, 294 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 487 g

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by 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 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.

Autoren/Hrsg.

Mckean, Henry

Moll, Victor

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

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.