2009, ISBN: 9780387094946

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 mo… More...

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. 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. Inhoud: Taal: en; Bindwijze: E-book; Oorspronkelijke releasedatum: 20 april 2009; Aantal pagina's: 522; Ebook Formaat: Adobe ePub; Illustraties: Met illustraties; Betrokkenen: Hoofdauteur: Joseph H. Silverman; Hoofduitgeverij: Springer; Lees mogelijkheden: Lees dit ebook op: Android (smartphone en tablet) , Kobo e-reader , Desktop (Mac en Windows) , iOS (smartphone en tablet) , Windows (smartphone en tablet); Overige kenmerken: Editie: 2; Studieboek: Ja; Verpakking hoogte: 37 mm; EAN: Engels | E-book | 9780387094946 | 20 april 2009 | 522 pagina's | Adobe ePub, Wetenschap & Natuur, Wiskunde, Meetkunde, Cijfertheorie, Boeken, Algebraische meetkunde, Springer<

ISBN: 9780387094946

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… More...

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., Springer<

2009, ISBN: 9780387094946

eBooks, eBook Download (PDF), 2nd ed. 2009, 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 b… More...

eBooks, eBook Download (PDF), 2nd ed. 2009, 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 New York], Seiten: 513, Springer New York, 2009<

ISBN: 9780387094946

*The Arithmetic of Elliptic Curves* / pdf eBook für 52.99 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wisse… More...

*The Arithmetic of Elliptic Curves* / pdf eBook für 52.99 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Mathematik, Springer-Verlag GmbH<

ISBN: 9780387094946

The Arithmetic of Elliptic Curves: ab 52.99 € eBooks > Fachthemen & Wissenschaft > Mathematik Springer-Verlag GmbH eBook als pdf, Springer-Verlag GmbH