| 书目名称 | Rational Points on Elliptic Curves |
| 编辑 | Joseph H. Silverman,John T. Tate |
| 视频video | |
| 概述 | Helps students appreciate the unity of modern mathematics by stressing the interplay of algebra, geometry, analysis, and number theory.Includes a wealth of exercises.Stresses accessibility of the mate |
| 丛书名称 | Undergraduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | .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 |
| 出版日期 | Textbook 2015Latest edition |
| 关键词 | ABC conjecture; Fermat‘s last theorem; Frey curves; complex multiplication; elliptic curve cryptography; |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-3-319-18588-0 |
| isbn_softcover | 978-3-319-30757-2 |
| isbn_ebook | 978-3-319-18588-0Series ISSN 0172-6056 Series E-ISSN 2197-5604 |
| issn_series | 0172-6056 |
| copyright | Springer International Publishing Switzerland 2015 |
发表于 2025-3-21 18:31:45
