Rational Points on Elliptic Curves / by Joseph H. Silverman, John Tate
(Undergraduate Texts in Mathematics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1992 |
| 本文言語 | 英語 |
| 大きさ | X, 281 p : online resource |
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| 内容注記 | I Geometry and Arithmetic II Points of Finite Order III The Group of Rational Points IV Cubic Curves over Finite Fields V Integer Points on Cubic Curves VI Complex Multiplication Appendix A Projective Geometry 1. Homogeneous Coordinates and the Projective Plane 2. Curves in the Projective Plane 3. Intersections of Projective Curves 4. Intersection Multiplicities and a Proof of Bezout’s Theorem Exercises List of Notation |
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| 一般注記 | In 1961 the second author deliv1lred a series of lectures at Haverford Col lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter est in the theory of elliptic curves for subjects ranging from cryptogra phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove |
| 著者標目 | *Silverman, Joseph H. author Tate, John author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry FREE:Mathematics FREE:Algebraic Geometry |
| 分 類 | DC23:516.35 |
| 巻冊次 | ISBN:9781475742527 
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| ISBN | 9781475742527 |
| URL | http://dx.doi.org/10.1007/978-1-4757-4252-7 |
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