Elliptic Curves: Function Theory, Geometry, Arithmetic (Paperback)

Elliptic Curves: Function Theory, Geometry, Arithmetic By Henry McKean, Victor Moll Cover Image
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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: 9780521658171
ISBN-10: 0521658179
Publisher: Cambridge University Press
Publication Date: August 13th, 1999
Pages: 298
Language: English