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1、ThispageintentionallyleftblankAnalyticMethodsforDiophantineEquationsandDiophantineInequalitiesHaroldDavenportwasoneofthetrulygreatmathematiciansofthetwen-tiethcentury.BasedonlectureshegaveattheUniversityofMichiganintheearly1960s,thisbookisconcernedwiththeuseofanalyticmethodsinthes
2、tudyofintegersolutionstoDiophantineequationsandDiophan-tineinequalities.Itprovidesanexcellentintroductiontoatimelessareaofnumbertheorythatisstillaswidelyresearchedtodayasitwaswhenthebookoriginallyappeared.ThethreemainthemesofthebookareWaring’sproblemandtherepresentationofintegersb
3、ydiagonalforms,thesolubilityinintegersofsystemsofformsinmanyvariables,andthesolubilityinintegersofdiagonalinequalities.Forthesecondeditionofthebookacomprehensiveforewordhasbeenaddedinwhichthreeleadingexpertsdescribethemoderncontextandrecentdevelopments.Acompletelistofreferenceshas
4、alsobeenadded.AnalyticMethodsforDiophantineEquationsandDiophantineInequalitiesSecondeditionH.DavenportThiseditioneditedandpreparedforpublicationbyT.D.BrowningOxfordUniversitycambridgeuniversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPr
5、essTheEdinburghBuilding,Cambridgecb22ru,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521605830©EstateofHaroldDavenport1963,2005Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovision
6、ofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2005isbn-13978-0-511-08086-9eBook(NetLibrary)isbn-100-511-08086-7eBook(NetLibrary)isbn-13978-0-521-60583-0paperbackisbn-100-5
7、21-60583-0paperbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternetwebsitesreferredtointhisbook,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.FirsteditionfirstpublishedbyCampusPublis
8、hers1963ContentsForewordpageviiWa
