资源描述：
《Elliptic Tales - Curves, Counting, and Number Theory》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、December13,2011Time:06:03pmfm.texEllipticTalesiThispageintentionallyleftblankDecember13,2011Time:06:03pmfm.texEllipticTalesCurves,Counting,andNumberTheory•••••AvnerAshRobertGrossPrincetonUniversityPressPrincetonandOxfordiiiCopyright©2012byPrincetonUniversityPressPublishedbyPrincetonUniversityP
2、ress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWpress.princeton.eduAllRightsReservedLibraryofCongressCataloging-in-PublicationDataAsh,Avner,1949Elliptictales:curves,counting,andnumbertheory/AvnerAsh,RobertGross.
3、p.cm.Includesbibliographicalreferencesandindex.ISBN978-0-691-15119-9(hardcover)1.Ellipticfunctions.2.Curves,Elliptic.3.Numbertheory.I.Gross,Robert,1959II.Title.QA343.A972012515.983dc232011044712BritishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinMinionProPrintedonac
4、id-freepaper.∞TypesetbySRNovaPvtLtd,Bangalore,IndiaPrintedintheUnitedStatesofAmerica13579108642ivForEdieandRosemaryvThispageintentionallyleftblankThanlongenfolktogononpilgrimages,Andpalmeresfortosekenstrangestrondes.GeoffreyChaucer,TheCanterburyTales•••••ThescienceofPureMathematics,initsmodern
5、developments,mayclaimtobethemostoriginalcreationofthehumanspirit....Theoriginalityofmathematicsconsistsinthefactthatinmathematicalscienceconnectionsbetweenthingsareexhibitedwhich,apartfromtheagencyofhumanreason,areextremelyunobvious.Thustheideas,nowinthemindsofcontemporarymathematicians,liever
6、yremotefromanynotionswhichcanbeimmediatelyderivedbyperceptionthroughthesenses.AlfredNorthWhitehead,ScienceandtheModernWorldviiThispageintentionallyleftblankDecember13,2011Time:06:03pmfm.texContents•••••PrefacexiiiAcknowledgmentsxixPrologue1PARTI.DEGREEChapter1.DegreeofaCurve131.GreekMathematic
7、s132.Degree143.ParametricEquations204.OurTwoDefinitionsofDegreeClash23Chapter2.AlgebraicClosures261.SquareRootsofMinusOne262.ComplexArithmetic283.RingsandFields304.ComplexNumbersandSolvingEquations325.Congruences346.ArithmeticModuloaPrim
