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1、SpringerMonographsinMathematicsGoroShimuraEEElementaryDirichletSeriesandModularFormsGoroShimuraDepartmentofMathematicsPrincetonUniversityPrinceton,NewJersey08544-1000goro@math.princeton.eduISBN:978-0-387-72473-7eISBN:978-0-387-72474-4LibraryofCongressControlNumber:2
2、007931368MathematicsSubjectClassification(2000):11F11,11F67,11G05,11G10,11G15,11R29,11M06©2007SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,
3、LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedi
4、sforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaper.987654321springer.comPREFACEAbookon
5、anymathematicalsubjectabovetextbooklevelisnotofmuchvalueunlessitcontainsnewideasandnewperspectives.Also,theauthormaybeencouragedtoincludenewresults,providedthattheyhelpthereadergainnewinsightsandarepresentedalongwithknownoldresultsinaclearexposition.Itiswiththisphil
6、osophythatIwritethisvolume.Thetwosubjects,Dirichletseriesandmodularforms,aretraditional,butItreattheminbothorthodoxandunorthodoxways.However,Itrytomakethebookaccessibletothosewhoarenotfamiliarwithsuchtopics,byincludingplentyofexpositorymaterial.Morespecificdescriptio
7、nsofthecontentswillbegivenintheIntroduction.Tosomeextent,thisbookhasasupplementarynaturetomypreviousbookIntroductiontotheArithmeticTheoryofAutomorphicFunctions,publishedbyPrincetonUniversityPressin1971,thoughIdonotwritethepresentbookwiththatintent.Whilethe1971bookgr
8、ewoutofmylecturesinvariousplaces,theessentialpointsofthisnewbookhaveneverbeenpresentedpubliclyorprivately.Ihopethatitwilldrawanaudienceasl
