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1、LectureNotesinMathematics1845Editors:J.--M.Morel,CachanF.Takens,GroningenB.Teissier,Paris3BerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoMinHoLeeMixedAutomorphicForms,TorusBundles,andJacobiForms13AuthorMinHoLEEDepartmentofMathematicsUniversityofNorthernIowaCedarFallsIA
2、50614,U.S.A.e-mail:lee@math.uni.eduLibraryofCongressControlNumber:2004104067MathematicsSubjectClassification(2000):11F11,11F12,11F41,11F46,11F50,11F55,11F70,14C30,14D05,14D07,14G35ISSN0075-8434ISBN3-540-21922-6Springer-VerlagBerlinHeidelbergNewYorkThisworkissubjecttocopyrig
3、ht.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermitte
4、donlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.Springer-VerlagisapartofSpringerScience+BusinessMediahttp://www.springe
5、ronline.comcSpringer-VerlagBerlinHeidelberg2004PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefre
6、eforgeneraluse.Typesetting:Camera-readyTEXoutputbytheauthorsSPIN:1100632941/3142/du-543210-Printedonacid-freepaperToVirginia,Jenny,andKatiePrefaceThisbookisconcernedwithvarioustopicsthatcenteraroundequivariantholomorphicmapsofHermitiansymmetricdomainsandisintendedforspe-cia
7、listsinnumbertheoryandalgebraicgeometry.Inparticular,itcontainsacomprehensiveexpositionofmixedautomorphicformsthathasneverap-pearedinbookform.Theperiodmapω:H→HofanellipticsurfaceEoveraRiemannsurfaceXisaholomorphicmapofthePoincar´eupperhalfplaneHintoitselfthatisequivariantwi
8、threspecttothemonodromyrepresentationχ:Γ→SL(2,R)ofthediscretesubgroupΓ⊂SL(2,R)dete
