The Arithmetic of Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Arithmetic of Elliptic Curves write by Joseph H. Silverman. This book was released on 2013-03-09. The Arithmetic of Elliptic Curves available in PDF, EPUB and Kindle. 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.
Advanced Topics in the Arithmetic of Elliptic Curves
Advanced Topics in the Arithmetic of Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advanced Topics in the Arithmetic of Elliptic Curves write by Joseph H. Silverman. This book was released on 2013-12-01. Advanced Topics in the Arithmetic of Elliptic Curves available in PDF, EPUB and Kindle. In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Rational Points on Elliptic Curves
Rational Points on Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rational Points on Elliptic Curves write by Joseph H. Silverman. This book was released on 2013-04-17. Rational Points on Elliptic Curves available in PDF, EPUB and Kindle. 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.
Elliptic Curves (Second Edition)
Elliptic Curves (Second Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Curves (Second Edition) write by James S Milne. This book was released on 2020-08-20. Elliptic Curves (Second Edition) available in PDF, EPUB and Kindle. This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer.Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work.The first three chapters develop the basic theory of elliptic curves.For this edition, the text has been completely revised and updated.
Elliptic Curves
Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Curves write by Henry McKean. This book was released on 1999-08-13. Elliptic Curves available in PDF, EPUB and Kindle. An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.
