Joseph H. Silverman, John Tate

Rational Points on Elliptic Curves (eBook, PDF)

• Format: PDF

Produktbeschreibung

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book's accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 281
• Erscheinungstermin: 17. April 2013
• Englisch
• ISBN-13: 9781475742527
• Artikelnr.: 43993544

Autorenporträt

Joseph H. Silverman is Professor of Mathematics at Brown University. He is the author of over 100 research articles and numerous books on elliptic curves, diophantine geometry, cryptography, and arithmetic dynamical systems. John T. Tate is Professor Emeritus of Mathematics at The University of Texas at Austin and at Harvard University. For his seminal contributions to number theory, he was awarded the 2010 Abel Prize.

Inhaltsangabe

Introduction.- Geometry and Arithmetic.- Points of Finite Order.- The Group of Rational Points.- Cubic Curves over Finite Fields.- Integer Points on Cubic Curves.- Complex Multiplication.

Rezensionen

"The two main changes for this edition are a new section on elliptic curve cryptography and an explanation of how elliptic curves played a role in the proof of Fermat's Last Theorem. ... the best place to start learning about elliptic curves." (Fernando Q. Gouvêa, MAA Reviews, maa.org, April, 2016)

"The book is an excellent introduction to elliptic curves over the rational numbers and ideal textbook for an undergraduate course. ... This book is highly recommended to students and researches interested in elliptic curves and their applications. It provides a natural step to a more advanced treatment of the subject." (Andrej Dujella, zbMATH 1346.11001, 2016)