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The Arithmetic of Elliptic Curves - Joseph H. Silverman
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2016, ISBN: 9780387094939

ID: 610388794

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, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell Weil theorem giving finite generation of the group of rational points and Siegel s theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra s factorization algorithm, Schoof s point counting algorithm, Miller s algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro s conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics. The theory of elliptic curves is distinguished by the diversity of the methods 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. Bücher > Fremdsprachige Bücher > Englische Bücher gebundene Ausgabe 25.03.2016 Buch (fremdspr.), Springer, .201

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The Arithmetic of Elliptic Curves - Joseph H. Silverman
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2009, ISBN: 0387094938

ID: 8750771342

[EAN: 9780387094939], Neubuch, [SC: 8.9], [PU: Springer-Verlag Gmbh Jun 2009], ARITHMETIK; KURVE (MATHEMATISCH), Neuware - 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, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell Weil theorem giving finite generation of the group of rational points and Siegel s theorem on finiteness of integral points.For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra s factorization algorithm, Schoof s point counting algorithm, Miller s algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro s conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics. 514 pp. Englisch

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The Arithmetic of Elliptic Curves
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The Arithmetic of Elliptic Curves: Hardback: Springer-Verlag New York Inc. : 9780387094939: 29 May 2009: The theory of elliptic curves is distinguished by the diversity of the methods 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 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. Algebraic Geometry, , , , , , , , , , , ,, [PU: Springer]

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The arithmetic of elliptic curves - Silverman, j.
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Silverman, j.:
The arithmetic of elliptic curves - neues Buch

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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., [PU: Springer]

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Details zum Buch
The Arithmetic of Elliptic Curves
Autor:

Silverman, Joseph H.

Titel:

The Arithmetic of Elliptic Curves

ISBN-Nummer:

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.

Detailangaben zum Buch - The Arithmetic of Elliptic Curves


EAN (ISBN-13): 9780387094939
ISBN (ISBN-10): 0387094938
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2009
Herausgeber: Springer-Verlag GmbH
514 Seiten
Gewicht: 0,888 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 15.11.2007 06:48:59
Buch zuletzt gefunden am 02.06.2017 06:34:07
ISBN/EAN: 9780387094939

ISBN - alternative Schreibweisen:
0-387-09493-8, 978-0-387-09493-9


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