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شنبه 19 شهریور 1390

Rational points on elliptic curves ebook

نویسنده: Konner Bauer   

Rational points on elliptic curves




Author: John Tate, Joseph H. Silverman
Type: eBook
Date Released: 1992
Format: djvu
Language: English
Page Count: 296
Isbn10 Code: 3540978259
Isbn13 Code: 9783540978251


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.

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