langlands, robert p.; jacquet, herve - automorphic forms on gl(2)

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1、AutomorphicFormsonGL(2)Herve´JacquetandRobertP.LanglandsFormerlyappearedasvolume#114intheSpringerLectureNotesinMathematics,1970,pp.1-548Chapter1iTableofContentsIntroduction...................................iiChapterI:LocalTheory...............................

2、1§1.Weilrepresentations.............................1§2.RepresentationsofGL(2,F)inthenon-archimedeancase...........15§3.Theprincipalseriesfornon-archimedeanfields................58§4.Examplesofabsolutelycuspidalrepresentations................77§5.Representation

3、sofGL(2,R)........................96§6.RepresentationofGL(2,C).........................138§7.Characters................................151§8.Oddsandends..............................173ChapterII:GlobalTheory.............................189§9.TheglobalHeckealge

4、bra..........................189§10.Automorphicforms............................204§11.Hecketheory...............................221§12.Someextraordinaryrepresentations.....................251ChapterIII:QuaternionAlgebras..........................267§13.Zeta-f

5、unctionsforM(2,F).........................267§14.Automorphicformsandquaternionalgebras.................294§15.Someorthogonalityrelations........................304§16.AnapplicationoftheSelbergtraceformula..................320Chapter1iiIntroductionTwoofthebestk

6、nownofHecke’sachievementsarehistheoryofL-functionswithgrossen-¨charakter,whichareDirichletserieswhichcanberepresentedbyEulerproducts,andhistheoryoftheEulerproducts,associatedtoautomorphicformsonGL(2).Sinceagrossencharakterisanautomorphic¨formonGL(1)oneistempte

7、dtoaskiftheEulerproductsassociatedtoautomorphicformsonGL(2)playaroleinthetheoryofnumberssimilartothatplayedbytheL-functionswithgrossencharakter.¨InparticulardotheybearthesamerelationtotheArtinL-functionsassociatedtotwo-dimensionalrepresentationsofaGaloisgroupa

8、stheHeckeL-functionsbeartotheArtinL-functionsassociatedtoone-dimensionalrepresentations?Althoughwecannotanswerthequestiondefinitivelyoneoftheprincipalpurposesofthesenotesistoprovide