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1、ANINTRODUCTIONTOTHETHEORYOFNUMBERSANINTRODUCTIONTOTHETHEORYOFNUMBERSBYG.H.HARDYANDE.M.WRIGHTPrincipalandVice-ChancelloroftheUniversityofAberdeenFOURTHEDITIONOX.FORDATTHECLARENDONPRESSOx@dUniversityPress,ElyHouse,LondonW.1OLASOOWNEWYORKTORONTOMELBOURNEWELLINGTONCAPETOWNIBADANNAIROB
2、IDARESSALAAMI.USAKAADDISABABADELEIBOMBAYC.4I.CUTTAMADRASKARACHILAHOREDACCAKUALALUMPURSINOAPOREHONORONOTOKYOISBN0198533107Fi&edition1938Secondeditionxg45Thirdedition1954Fourthedition1960rg6z(withcorrections)1965(withcorrections)1968(withcowectiona)=97=>1975PrintedinGreatB&ainattheU
3、niversityPress,OxfordbyVivianRidlerPrintertotheUniversityPREFACETOTHEFOURTHEDITIONAPARTfromtheprovisionofanindexofnames,themainchangesinthiseditionareintheNotesattheendofeachchapter.Thesehavebeenrevisedtoincludereferencestoresultspublishedsincethethirdeditionwenttopressandtocorrec
4、tomissions.ThercaresimplerproofsofTheorems234,352,and357andanewTheorem272.ThePostscripttothethirdeditionnowtakesitsproperplaceaspartofChapterXX.1amindebtedtoseveralcorrespondentswhosuggestedimprovementsandcorrections.1havetothankDr.PontingforagainreadingtheproofsandMrs.V.N.R.Milne
5、forcompilingtheindexofnames.E.M.W.ABERDEENJuly1959PREFACETOTHEFIRSTEDITIONTHISbookhasdevelopedgraduallyfromlecturesdeliveredinanumberofuniversitiesduringthelasttenyears,and,likemanybookswhichhavegrownoutoflectures,ithasnoverydefiniteplan.Itisnotinanysense(asanexpertcariseebyreadin
6、gthetableofcontents)asystematictreatiseonthetheoryofnumbers.Itdoesnotevencontainafullyreasonedaccountofanyonesideofthatmany-sidedtheory,butisanintroduction,oraseriesofintroductions,toalmosta11ofthesesidesinturn.Wesaysomethingabouteachofanumberofsubjectswhicharenotusuallycombinedin
7、asinglevolume,andaboutsomewhicharenotalwaysregardedasformingpartofthetheoryofnumbersatall.ThusChs.XII-XVbelongtothe‘algebraic’theoryofnumbers,Chs.XIX-XXItothe‘additive’,andCh.XXIItothe‘analytic’theories;whileChs.III,XI,XXIII,andXXIVdealwithmattersusuallyclassifiedundertheheadingso
8、f‘geometryofnumbers’or‘Diophantin
