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1、SpringerMonographsinMathematics1J.CoatesR.Sujatha.CyclotomicFieldsandZetaValues1232J.CoatesCentreforMathematicalSciencesDPMMSWilberforceRoadCambridge,CB30WB,Englande-mail:J.H.Coates@dpmms.cam.ac.ukR.SujathaSchoolofMathematicsTataInstituteofFundamentalResearchHomiBhabh
2、aRoad,ColabaMumbai400005,Indiae-mail:sujatha@math.tifr.res.inLibraryofCongressControlNumber:2006927549MathematicsSubjectClassification(2000):11R18,11R23ISSN1439-7382ISBN-103-540-33068-2SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-33068-4SpringerBerlinHeidelbergNewY
3、orkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthis
4、publicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+Busi
5、nessMediaspringer.com©Springer-VerlagBerlinHeidelberg2006Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefree
6、forgeneraluse.TypesettingbytheauthorsandSPiusingaSpringerLATEXmacropackageCoverdesign:ErichKirchner,Heidelberg,GermanyPrintedonacid-freepaperSPIN:1168585241/3100/SPi-5432103PrefaceChihayaburuMightytheyareKaminoigakiniThegodswithinthissacredshrine-HaukuzumoYeteventhevi
7、nesAkiniwaaezuCreepingintheprecinctscouldnotholdUtsuroinikeriAgainsttheautumn’stingeingoftheirleaves.–KinoTsurayaki(Kokinshu,V:262).Thislittlebookisintendedforgraduatestudentsandthenon-expertinIwasawatheory.Itsaimistopresentinfulldetailthesimplestproofoftheimportantth
8、eoremoncyclotomicfields,whichisoftencalled“themainconjecture”.Wehavethoughtitworthwhiletowritesuchabook,notonlybecausethisthe
