Joseph H. Silverman, John Tate

Rational Points on Elliptic Curves (eBook, PDF)

• Format: PDF

Produktbeschreibung

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. "Rational Points on Elliptic Curves" stresses this interplay as it develops the basic theory, thereby providing an opportunity for advance 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.

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Produktdetails

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

Autorenporträt

Dr. Jeffrey Hoffstein has been a professor at Brown University since 1989 and has been a visiting professor and tenured professor at several other universities since 1978. His research areas are number theory, automorphic forms and cryptography. He has authored more than 50 publications. Dr. Jill Pipher has been a professor at Brown University since 1989. She has been an invited lecturer and has received numerous awards and honors. Her research areas are harmonic analysis, elliptic PDE, and cryptography. She has authored over 40 publications. Dr. Joseph Silverman has been a professor at Brown University since 1988. He served as the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards and is a frequently invited lecturer. His research areas are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has authored more than 130 publications and has had more than 20 doctoral students.

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)