Introduction to Elliptic Curves and Modular Forms

Neal I. Koblitz

ISBN 10: 0387979662 / ISBN 13: 9780387979663

Verlag: Springer-Verlag New York Inc., US, 1993

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. Bestandsnummer des Verkäufers LU-9780387979663

Inhaltsangabe:

The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.

Bibliografische Details

Titel: Introduction to Elliptic Curves and Modular ...
Verlag: Springer-Verlag New York Inc., US
Erscheinungsdatum: 1993
Einband: Hardback
Zustand: New
Auflage: 2nd ed. 1993.