A Classical Introduction to Modern Number Theory / by Kenneth Ireland, Michael Rosen
(Graduate Texts in Mathematics ; 84)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1990 |
| 本文言語 | 英語 |
| 大きさ | XIV, 394 p : online resource |
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| 内容注記 | 1 Unique Factorization 2 Applications of Unique Factorization 3 Congruence 4 The Structure of U(?/n?) 5 Quadratic Reciprocity 6 Quadratic Gauss Sums 7 Finite Fields 8 Gauss and Jacobi Sums 9 Cubic and Biquadratic Reciprocity 10 Equations over Finite Fields 11 The Zeta Function 12 Algebraic Number Theory 13 Quadratic and Cyclotomic Fields 14 The Stickelberger Relation and the Eisenstein Reciprocity Law 15 Bernoulli Numbers 16 Dirichlet L-functions 17 Diophantine Equations 18 Elliptic Curves 19 The Mordell-Weil Theorem 20 New Progress in Arithmetic Geometry Selected Hints for the Exercises |
|---|---|
| 一般注記 | Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves |
| 著者標目 | *Ireland, Kenneth author Rosen, Michael author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Number theory FREE:Mathematics FREE:Number Theory |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9781475721034 
|
| ISBN | 9781475721034 |
| URL | http://dx.doi.org/10.1007/978-1-4757-2103-4 |
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