内容简介
Thepurposeofthesenoteswouldhavebeenbetterexplainedifwehadchosenanothertitle，namely，Jacquet-Langlands'TheoryMadeEasy；itoccurredtousatthelastmomentthatamorepedestrianchoicewouldbemoreprudent，sinceafteralltheauthorisinaratherbadpositiontojudge.
ThesenotescoveraverylargepartofChapters2，3，5，6，9，10and11ofJacquet-Langlands'work，AutomorphicFormsonGL（2），VII+548pp.，1970，Springer（LectureNotesinMathematics，No.114）.Sincethevolumeofournotesisaboutonefifthof548pp.，itisnottobeexpectedthatwehavebeenableheretoexplaineverything.Infact，wehaveentirelyomittedtheexplicitconstructionofdiscreteseriesfromquadraticextensionsorquaternionalgebra（Chapter4ofJacquetandLanglands），theconnectionwithZetafunctionsofmatrixalgebras（Chapter13），andthemostinteresting，oratanyratenewest，partoftheirwork，namely，therelationsbetweenthe"spectra"ofaquaternionalgebraanda2×2matrixalgebra.ThereaderwhoissufficientlyinterestedbythepresentnoteswillofcoursehavetogobacktoJacquetandLanglandsanyway.
WehavegivenfullproofsinChapter1andnearlycompleteonesinChapter3，butnotinChapter2.Forthebibliography，wereferthereadertoJacquetandLanglands，wherereferenceswillbefound.
ThesenoteshavebeenwrittenafterlecturesonthesamesubjectatTheInstituteforAdvancedStudy，wherewefound，fromSeptember，1969toApril，1970，averywelcomeatmosphereofquietintellectualwork.Itisforusagreatpleasuretoexpresshereourdeepgratitudenotonlyfortheconvenienceswewereprovidedwith，butalsoforthefactthatweweresparedthedutytothanktheU.S.AirForceforitsmaincontributiontoCultureandCivilization，namely，thehighlypalatableNapalm-and-Mathematicscocktailthatisthemarkofthetimesinthemostadvancedcountryoftheworld.目录
前言/序言
Thepurposeofthesenoteswouldhavebeenbetterexplainedifwehadchosenanothertitle，namely，Jacquet-Langlands'TheoryMadeEasy；itoccurredtousatthelastmomentthatamorepedestrianchoicewouldbemoreprudent，sinceafteralltheauthorisinaratherbadpositiontojudge.
ThesenotescoveraverylargepartofChapters2，3，5，6，9，10and11ofJacquet-Langlands'work，AutomorphicFormsonGL（2），VII+548pp.，1970，Springer（LectureNotesinMathematics，No.114）.Sincethevolumeofournotesisaboutonefifthof548pp.，itisnottobeexpectedthatwehavebeenableheretoexplaineverything.Infact，wehaveentirelyomittedtheexplicitconstructionofdiscreteseriesfromquadraticextensionsorquaternionalgebra（Chapter4ofJacquetandLanglands），theconnectionwithZetafunctionsofmatrixalgebras（Chapter13），andthemostinteresting，oratanyratenewest，partoftheirwork，namely，therelationsbetweenthe"spectra"ofaquaternionalgebraanda2×2matrixalgebra.ThereaderwhoissufficientlyinterestedbythepresentnoteswillofcoursehavetogobacktoJacquetandLanglandsanyway.
WehavegivenfullproofsinChapter1andnearlycompleteonesinChapter3，butnotinChapter2.Forthebibliography，wereferthereadertoJacquetandLanglands，wherereferenceswillbefound.
ThesenoteshavebeenwrittenafterlecturesonthesamesubjectatTheInstituteforAdvancedStudy，wherewefound，fromSeptember，1969toApril，1970，averywelcomeatmosphereofquietintellectualwork.Itisforusagreatpleasuretoexpresshereourdeepgratitudenotonlyfortheconvenienceswewereprovidedwith，butalsoforthefactthatweweresparedthedutytothanktheU.S.AirForceforitsmaincontributiontoCultureandCivilization，namely，thehighlypalatableNapalm-and-Mathematicscocktailthatisthemarkofthetimesinthemostadvancedcountryoftheworld.
