Rational Points On Elliptic Curves
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Rational Points On Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer
Release Date : 2015-06-02
Rational Points On Elliptic Curves written by Joseph H. Silverman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-02 with Mathematics categories.
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced 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. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Rational Points On Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-11-18
Rational Points On Elliptic Curves written by Joseph H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-18 with Mathematics categories.
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Rational Points On Modular Elliptic Curves
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Author : Henri Darmon
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Rational Points On Modular Elliptic Curves written by Henri Darmon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Rational Points On Elliptic Curves
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Author : David Grant
language : en
Publisher:
Release Date : 1981
Rational Points On Elliptic Curves written by David Grant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Rational Points On Elliptic Curves
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Author : Kendra Hershey
language : en
Publisher:
Release Date : 1993
Rational Points On Elliptic Curves written by Kendra Hershey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Elliptic Curves And Their Arithmetic Geometry
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-07-28
Elliptic Curves And Their Arithmetic Geometry written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-28 with Mathematics categories.
EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.
The Rational Points On Elliptic Curves
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Author : Julian Rojter
language : en
Publisher:
Release Date : 1974
The Rational Points On Elliptic Curves written by Julian Rojter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Elliptic Curves
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Author : Dale Husemöller
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
Elliptic Curves written by Dale Husemöller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices
Rational Points On Elliptic Curves Over Function Fields
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Author : Thomas Russell Bolton
language : en
Publisher:
Release Date : 2008
Rational Points On Elliptic Curves Over Function Fields written by Thomas Russell Bolton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Arithmetical algebraic geometry categories.
Rational Points On Elliptic Curves Over Finite Fields
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Author : 黃柏嶧
language : en
Publisher:
Release Date : 1999
Rational Points On Elliptic Curves Over Finite Fields written by 黃柏嶧 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.