Rational Points on Elliptic Curves PDF

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AUTEUR: Joseph H. Silverman

TAILLE DU FICHIER: 3,89 MB

NOM DE FICHIER: Rational Points on Elliptic Curves.pdf

ISBN: 9783319185873

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The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask fora description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book Topics covered incude the geometry and group structure of elliptic curves, the Nagell-Lutz theorem describing points of finite order, the Mordell-Weil theorem on the finite generation of the group of rational points, the Thue-Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.

INFORMATION

AUTEUR: Joseph H. Silverman

TAILLE DU FICHIER: 4,97 MB

NOM DE FICHIER: Rational Points on Elliptic Curves.pdf

ISBN: 9783319185873

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Téléchargez la version électronique de Rational Points on Elliptic Curves sur rhonealpesinfo.fr. Formats disponibles : Rational Points on Elliptic Curves PDF, Rational Points on Elliptic Curves ePUB, Rational Points on Elliptic Curves MOBI

Rational Points on Elliptic Curves. Authors: Silverman, Joseph H., Tate, John T. Show next edition Free Preview. Buy this book ... In 1961 the second author deliv1lred a series of lectures at Haverford Col­ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran­ scribed, and printed in mimeograph form ...

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