Rational Points on Elliptic Curves - Rilegato

Silverman, Joseph H.; Tate, John

Rilegato

ISBN 10: 3540978259 ISBN 13: 9783540978251

Casa editrice: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Riassunto

The emphasis of this text is on the number-theoretic aspects of elliptic curves. Using an informal style, the authors attempt to present a mathematically difficult field in a readable manner. The first part is devoted to proving the fundamental theorems of the field (or at least special cases of these): The Nagell-Lutz theorem, Mordell's theorem, and Hasse's theorem. The remainder of the book discusses special topics and newer developments. A discussion of Lara's algorithm for factoring large numbers shows an application of elliptic curves to the "real world", in this case, the problem of public-key cryptographic systems. A proof of Siegel's theorem, which asserts that an elliptic curve has only a finite number of integer points, serves to introduce the powerful notions of Diophantine approximation techniques. A final chapter introduces the theory of complex multiplication and discusses how points of finite order on elliptic curves can be used to generate extension fields with Abelian Galois groups. The book can readily be used for a one-semester course; parts of it can also serve as the basis for a supplementary topic at the end of a traditional course in either aalgebraic geometry or number theory. Many exercises are included, ranging from easy calculations to the published theorems.

Su questo libro

Product Description:

Book by Silverman Joseph H Tate John

Su questa edizione

• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Data di pubblicazione: 1992
• ISBN 10: 3540978259
• ISBN 13: 9783540978251
• Rilegatura: Copertina rigida
• Numero di pagine: 291