The Arithmetic of Elliptic Curves

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Beschreibung

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Über den Autor

Dr. Joseph Silverman is a professor at Brown University and has been an instructor or professors since 1982. He was the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards, as well as being a frequently invited lecturer. He is currently a member of the Council of the American Mathematical Society. His research areas of interest are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has co-authored over 120 publications and has had over 20 doctoral students under his tutelage. He has published 9 highly successful books with Springer, including the recently released, An Introduction to Mathematical Cryptography, for Undergraduate Texts in Mathematics.

Zusammenfassung

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX.

Inhaltsverzeichnis

Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell#x2013;Weil Group.- Algorithmic Aspects of Elliptic Curves.

Details

Erscheinungsjahr:	2009
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xx 513 S. 14 s/w Illustr. 513 p. 14 illus.
ISBN-13:	9780387094939
ISBN-10:	0387094938
Sprache:	Englisch
Herstellernummer:	12270347
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Silverman, Joseph H.
Auflage:	2nd ed. 2009
Hersteller:	Springer US Springer New York Springer US, New York, N.Y. Graduate Texts in Mathematics
Maße:	241 x 160 x 35 mm
Von/Mit:	Joseph H. Silverman
Erscheinungsdatum:	29.05.2009
Gewicht:	0,963 kg

Artikel-ID: 101642962

Über den Autor

Zusammenfassung

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2009
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xx 513 S. 14 s/w Illustr. 513 p. 14 illus.
ISBN-13:	9780387094939
ISBN-10:	0387094938
Sprache:	Englisch
Herstellernummer:	12270347
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Silverman, Joseph H.
Auflage:	2nd ed. 2009
Hersteller:	Springer US Springer New York Springer US, New York, N.Y. Graduate Texts in Mathematics
Maße:	241 x 160 x 35 mm
Von/Mit:	Joseph H. Silverman
Erscheinungsdatum:	29.05.2009
Gewicht:	0,963 kg