| 书目名称 | Diophantine m-tuples and Elliptic Curves |
| 编辑 | Andrej Dujella |
| 视频video | |
| 概述 | A unique mixture of classical mathematics and recent research.Present solutions of problems that were open for centuries.Provides an attractive introduction to elliptic curves for students |
| 丛书名称 | Developments in Mathematics |
| 图书封面 |  |
| 描述 | .This book provides an overview of the main results and problems concerning Diophantine .m.-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators...The book presents fragments of the history of Diophantine .m.-tuples, emphasising the connections between Diophantine .m.-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine .m.-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine .m.-tuples are used to construct elliptic curves with interesting Mordell–Weil groups, including curves of record rank with agiven torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems...This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. Ho |
| 出版日期 | Book 2024 |
| 关键词 | Diophantine Equations; Diophantine Quadruples; Elliptic Curves; Torsion Group; Rank of Elliptic Curves; A |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-56724-7 |
| isbn_softcover | 978-3-031-56726-1 |
| isbn_ebook | 978-3-031-56724-7Series ISSN 1389-2177 Series E-ISSN 2197-795X |
| issn_series | 1389-2177 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 16:08:03
