椭圆曲线的有理点

图书标准信息

• 作者 [美]西尔弗曼（Silverman J.H.） 著
• 出版社 世界图书出版公司
• 出版时间 2015-01
• 版次 1
• ISBN 9787510086328
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 281页
• 正文语种 英语

【内容简介】

　　Thetheoryofellipticcurvesinvolvesablendofalgebra，geometry，analysis，andnumbertheory.Thisbookstressesthisinterplayasitdevelopsthebasictheory，providinganopportunityforreaderstoappreciatetheunityofmodernmathematics.Thebooksaccessibility，theinformalwritingstyle，andawealthofexercisesmakeitanidealintroductionforthoseinterestedinlearningaboutDiophantineequationsandarithmeticgeometry.

【目录】

Preface
ComputerPackages
Acknowledgments
Introduction
CHAPTER1
GeometryandArithmetic
1.RationalPointsonConics
2.TheGeometryofCubicCurves
3.WeierstrassNormalForm
4.ExplicitFormulasfortheGroupLaw
Exercises

CHAPTER2
PointsofFiniteOrder
1.PointsofOrderTwoandThree
2.RealandComplexPointsonCubicCurves
3.TheDiscriminant
4.PointsofFiniteOrderHaveIntegerCoordinates
5.TheNagell—LutzTheoremandFurtherDevelopments
Exercises

CHAPTER3
TheGroupofRationalPoints
1.HeightsandDescent
2.TheHeightofP+P0
3.TheHeightof2P
4.AUsefulHomomorphism
5.Mordell'sTneorem
6.ExamplesandFurtherDevelopments
7.SingularCubicCurves
Exercises

CHAPTER4
CubicCurvesoverFiniteFields
1.RationalPointsoverFiniteFields
2.ATheoremofGauss
3.PointsofFiniteOrderRevisited
4.AFactorizationAlgorithmUsingEllipticCurves
Exercises

CHAPTER5
IntegerPointsonCubicCurves
1.HowManyIntegerPoints？
2.TaxicabsandSumsofTwoCubes
3.Thue'sTheoremandDiophantineApproximation
4.ConstructionofanAuxiliaryPolynomial
5.TheAuxiliaryPolynomiallsSmall
6.TheAuxiliaryPolynomialDoesNotVanish
7.ProofoftheDiophantineApproximationTheorem
8.FurtherDevelopments
Exercises

CHAPTER6
ComplexMultiplication
1.AbelianExtensionsofQ
2.AlgebraicPointsonCubicCurves
3.AGaloisRepresentation
4.ComplexMultiplication
5.AbelianExtensionsofQ（i）
Exercises

APPENDIXA
ProjectiveGeometry
1.HomogeneousCoordinatesandtheProjectivePlane
2.CurvesintheProjectivePlane
3.IntersectionsofProjectiveCurves
4.IntersectionMultiplicitiesandaProofofBezout'sTheorem
5.ReductionModulop
Exercises
Bibliography
ListofNotation
Index