An edition of The arithmetic of elliptic curves (1985)

The arithmetic of elliptic curves

2nd ed.
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March 28, 2025 | History
An edition of The arithmetic of elliptic curves (1985)

The arithmetic of elliptic curves

2nd ed.
  • 1 Want to read
  • 1 Currently reading

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.

Publish Date
Publisher
Springer
Language
English
Pages
513

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Previews available in: English

Edition Availability
Cover of: The arithmetic of elliptic curves
The arithmetic of elliptic curves
2009, Springer
in English - 2nd ed.
Cover of: The arithmetic of elliptic curves
The arithmetic of elliptic curves
2009, Springer
in English - 2nd ed.
Cover of: The arithmetic of elliptic curves
The arithmetic of elliptic curves
1986, Springer-Verlag
in English
Cover of: The arithmetic of elliptic curves
The arithmetic of elliptic curves
1985, Springer-Verlag
in English

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Book Details


Edition Notes

Includes bibliographical references (p. 473-487) and index.

Published in
New York, NY
Series
Graduate texts in mathematics -- 106

Classifications

Library of Congress
QA567 .S44 2009

The Physical Object

Pagination
xx, 513 p. :
Number of pages
513

Edition Identifiers

Open Library
OL23718966M
ISBN 13
9780387094939
LCCN
2009926474

Work Identifiers

Work ID
OL3275856W

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
March 28, 2025 Edited by ImportBot Redacting ocaids
May 20, 2020 Edited by CoverBot Added new cover
July 29, 2014 Edited by ImportBot import new book
April 6, 2014 Edited by ImportBot Added IA ID.
September 19, 2009 Created by ImportBot Imported from Library of Congress MARC record