橢圓麯綫的有理點 [Rational Points on Elliptic Curves]

橢圓麯綫的有理點 [Rational Points on Elliptic Curves] 下載 mobi epub pdf 電子書 2024


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[美] 西爾弗曼(Silverman J.H.) 著



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圖書介紹

齣版社: 世界圖書齣版公司
ISBN:9787510086328
版次:1
商品編碼:11647744
包裝:平裝
外文名稱:Rational Points on Elliptic Curves
開本:24開
齣版時間:2015-01-01
用紙:膠版紙
頁數:281
正文語種:英文


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圖書描述

內容簡介

  The theory of elliptic curves involves a blend of algebra,geometry, analysis,and number theory.This book stresses this interplay as it develops the basic theory,providing an opportunity for readers to appreciate the unity of modern mathematics.The book s accessibility,the informal writing style,and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

內頁插圖

目錄

Preface
Computer Packages
Acknowledgments
Introduction
CHAPTER 1
Geometry and Arithmetic
1.Rational Points on Conics
2.The Geometry of Cubic Curves
3.Weierstrass Normal Form
4.Explicit Formulas for the Group Law
Exercises

CHAPTER 2
Points of Finite Order
1.Points of Order Two and Three
2.Real and Complex Points on Cubic Curves
3.The Discriminant
4.Points of Finite Order Have Integer Coordinates
5.The Nagell—Lutz Theorem and Further Developments
Exercises

CHAPTER 3
The Group of Rational Points
1.Heights and Descent
2.The Height of P + P0
3.The Height of 2P
4.A Useful Homomorphism
5.Mordell's Tneorem
6.Examples and Further Developments
7.Singular Cubic Curves
Exercises

CHAPTER 4
Cubic Curves over Finite Fields
1.Rational Points over Finite Fields
2.A Theorem of Gauss
3.Points of Finite Order Revisited
4.A Factorization Algorithm Using Elliptic Curves
Exercises

CHAPTER 5
Integer Points on Cubic Curves
1.How Many Integer Points?
2.Taxicabs and Sums of Two Cubes
3.Thue's Theorem and Diophantine Approximation
4.Construction of an Auxiliary Polynomial
5.The Auxiliary Polynomialls Small
6.The Auxiliary Polynomial Does Not Vanish
7.Proof of the Diophantine Approximation Theorem
8.Further Developments
Exercises

CHAPTER 6
Complex Multiplication
1.Abelian Extensions of Q
2.Algebraic Points on Cubic Curves
3.A Galois Representation
4.Complex Multiplication
5.Abelian Extensions of Q(i)
Exercises

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
5.Reduction Modulo p
Exercises
Bibliography
List of Notation
Index

前言/序言



橢圓麯綫的有理點 [Rational Points on Elliptic Curves] 下載 mobi epub pdf txt 電子書 格式

橢圓麯綫的有理點 [Rational Points on Elliptic Curves] mobi 下載 pdf 下載 pub 下載 txt 電子書 下載 2024

橢圓麯綫的有理點 [Rational Points on Elliptic Curves] 下載 mobi pdf epub txt 電子書 格式 2024

橢圓麯綫的有理點 [Rational Points on Elliptic Curves] 下載 mobi epub pdf 電子書
想要找書就要到 圖書大百科
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

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還行,不錯。。。。。。。。

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橢圓麯綫的有理點 [Rational Points on Elliptic Curves] mobi epub pdf txt 電子書 格式下載 2024


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