资源描述：
《coates et al (eds) - arithmetic theory of elliptic curves (springer lnm 1716, 1999)》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、J.CoatesR.GreenbergK.A.RibetK.RubinArithmeticTheoryofElliptic~urves-Lecturesgivenatthe3rdSessionoftheCentroInternazionaleMatematicoEstivo(C.I.M.E.)heldinCetraro,Italy,July12-19,1997Editor:C.ViolaFonduiioneC.I.M.E.SpringerBerlinHeidelbergNewYorkBarcelonaHongKon
2、gLondonMilanParisSpringerSingaporeTokyoAuthorsJohnH.CoatesRalphGreenbergPrefaceDepartmentofPureMathematicsDepartmentofMathematicsandMathematicalStatisticsUniversityofWashingtonUniversityofCambridgeSeattle,WA98195,USA16MillLaneCambridgeCB21SB,UKTheC.I.M.E.Sessi
3、on"ArithmeticTheoryofEllipticCurves"washeldatKennethA.RibetKarlRubinCetraro(Cosenza,Italy)fromJuly12toJuly19,1997.DepartmentofMathematicsDepartmentofMathematicsThearithmeticofellipticcurvesisarapidlydevelopingbranchofUniversityofCaliforniaStanfordUniversityBer
4、keleyCA94720,USAStanfordCA94305,USAmathematics,attheboundaryofnumbertheory,algebra,arithmeticalge-braicgeometryandcomplexanalysis.~fterthepioneeringresearchinthisEditorfieldintheearlytwentiethcentury,mainlyduetoH.Poincar6andB.Levi,CarloViolatheoriginofthemoder
5、narithmetictheoryofellipticcurvesgoesbacktoDipartimentodiMatematicaL.J.Mordell'stheorem(1922)statingthatthegroupofrationalpointsonUniversitidiPisaanellipticcurveisfinitelygenerated.Manyauthorsobtainedinmorere-ViaBuonarroti2centyearscrucialresultsonthearithmeti
6、cofellipticcurves,withimportant56127Pisa,ItalyconnectionstothetheoriesofmodularformsandL-functions.AmongthemainproblemsinthefieldoneshouldmentiontheTaniyama-Shimuracon-jecture,whichstatesthateveryellipticcurveoverQismodular,andtheBirchandSwinnerton-Dyerconject
7、ure,which,initssimplestform,assertsCataloging-in-PublicationDataappliedforthattherankoftheMordell-WeilgroupofanellipticcurveequalstheorderofDieDeutscheBibliothek-CIP-EinheitsaufnahmevanishingoftheL-functionofthecurveat1.Newimpetustothearithmeticofellipticcurve
8、swasrecentlygivenbythecelebratedtheoremofA.Wiles(1995),whichprovestheTaniyama-Shimuraconjectureforsemistableellip-Arithmetictheoryofellipticcurves:heldinCetraro,Italy,Julyticcurves
