Introduction to Elliptic Curves and Modular Forms

Graduate Texts in Mathematics #97

by Neal Koblitz

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under­ standing of some basic tools used throughout mathematics. Graduate stu­ dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under­ graduates could use the book for independent study projects, senior theses, and seminar work.

Genres: Mathematics

262 pages, Hardcover

First published October 31, 1984

Reviews

[Wissam Raji · Rating 5 out of 5]

One of the classics on the theory of elliptic curves and modular forms. It gives a nice introduction to the theory od Weierstrass elliptic curves, rational points on elliptic curves, and slightly advanced topics in the theory. One special aspect of this book is the smooth treatment of the theory of modular forms of half-integer weight.