automorphic forms on gl(2) - h. jacquet, r. langlands

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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§

3、5.RepresentationsofGL(2,R)........................96§6.RepresentationofGL(2,C).........................138§7.Characters................................151§8.Oddsandends..............................173ChapterII:GlobalTheory.............................

4、189§9.TheglobalHeckealgebra..........................189§10.Automorphicforms............................204§11.Hecketheory...............................221§12.Someextraordinaryrepresentations.....................251ChapterIII:QuaternionAlgebras.......

5、...................267§13.Zeta-functionsforM(2,F).........................267§14.Automorphicformsandquaternionalgebras.................294§15.Someorthogonalityrelations........................304§16.AnapplicationoftheSelbergtraceformula................

6、..320Chapter1iiIntroductionTwoofthebestknownofHecke’sachievementsarehistheoryofL-functionswithgrossen-¨charakter,whichareDirichletserieswhichcanberepresentedbyEulerproducts,andhistheoryoftheEulerproducts,associatedtoautomorphicformsonGL(2).Sinceagrosse

7、ncharakterisanautomorphic¨formonGL(1)oneistemptedtoaskiftheEulerproductsassociatedtoautomorphicformsonGL(2)playaroleinthetheoryofnumberssimilartothatplayedbytheL-functionswithgrossencharakter.¨InparticulardotheybearthesamerelationtotheArtinL-functionsa

8、ssociatedtotwo-dimensionalrepresentationsofaGaloisgroupastheHeckeL-functionsbeartotheArtinL-functionsassociatedtoone-dimensionalrepresentations?Althoughwecannotanswerthequestiondefinitivelyoneoftheprincipalpurposesofthesenotesistoprovide