東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ subject:"Diophantine analysis." ]

切換: 標籤 | MARC模式 | ISBD

Rational points on elliptic curves

Silverman, Joseph H.

FindBook

Google Book

Amazon

博客來

Rational points on elliptic curves

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Rational points on elliptic curves/ by Joseph H. Silverman, John T. Tate.
作者:	Silverman, Joseph H.
其他作者:	Tate, John T.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	xxii, 332 p. :ill., digital ;24 cm.
內容註:	Introduction -- Geometry and Arithmetic -- Points of Finite Order -- The Group of Rational Points -- Cubic Curves over Finite Fields -- Integer Points on Cubic Curves -- Complex Multiplication.
Contained By:	Springer eBooks
標題:	Curves, Elliptic. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-18588-0
ISBN:	9783319185880 (electronic bk.)

Rational points on elliptic curves
Silverman, Joseph H.

Rational points on elliptic curves[electronic resource] /by Joseph H. Silverman, John T. Tate. - 2nd ed. - Cham :Springer International Publishing :2015. - xxii, 332 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,0172-6056. - Undergraduate texts in mathematics..

Introduction -- Geometry and Arithmetic -- Points of Finite Order -- The Group of Rational Points -- Cubic Curves over Finite Fields -- Integer Points on Cubic Curves -- Complex Multiplication.

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book 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 this book. 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 of the group of rational points, the Thue-Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.

ISBN: 9783319185880 (electronic bk.)

Standard No.: 10.1007/978-3-319-18588-0doiSubjects--Topical Terms:

540506
Curves, Elliptic.

LC Class. No.: QA567.2.E44

Dewey Class. No.: 516.352

Rational points on elliptic curves
LDR:02929nam a2200337 a 4500 001 2007810
003 DE-He213
005 20160122105537.0
006 m d
007 cr nn 008maaau
008 160219s2015 gw s 0 eng d
020 $a 9783319185880 (electronic bk.)
020 $a 9783319185873 (paper)
024 7 $a 10.1007/978-3-319-18588-0 $2 doi
035 $a 978-3-319-18588-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA567.2.E44
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
082 0 4 $a 516.352 $2 23
090 $a QA567.2.E44 $b S587 2015
100 1 $a Silverman, Joseph H. $3 808196
245 1 0 $a Rational points on elliptic curves $h [electronic resource] / $c by Joseph H. Silverman, John T. Tate.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xxii, 332 p. : $b ill., digital ; $c 24 cm.
490 1 $a Undergraduate texts in mathematics, $x 0172-6056
505 0 $a Introduction -- Geometry and Arithmetic -- Points of Finite Order -- The Group of Rational Points -- Cubic Curves over Finite Fields -- Integer Points on Cubic Curves -- Complex Multiplication.
520 $a The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book 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 this book. 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 of the group of rational points, the Thue-Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
650 0 $a Curves, Elliptic. $3 540506
650 0 $a Rational points (Geometry) $3 811921
650 0 $a Diophantine analysis. $3 540536
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Data Structures, Cryptology and Information Theory. $3 891008
700 1 $a Tate, John T. $3 2156835
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Undergraduate texts in mathematics. $3 1041596
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-18588-0
950 $a Mathematics and Statistics (Springer-11649)