introduction to analytic number theory - apostol

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1、UndergraduateTextsinMathematicsEdilorsF.W.GehringP.R.HalmosAdvisoryBoardC.DePrimaI.HersteinJ.KieferW.LeVequeTomM.ApostolIntroductiontoAnalyticNumberTheorySpringer-VerlagNewYorkHeidelbergBerlin1976TomM.ApostolProfessorofMathematicsCaliforniaInstituteofTechnologyPasadena.

2、California91I25AMSSubjectClassification(1976)10-01,1OAXXLibraryofCongressCataloginginPublicationDataApostol,TomM.Introductiontoanalyticnumbertheory.(Undergraduatetextsinmathematics)”Evolvedfromacourse(Mathematics160)offeredattheCaliforniaInstituteofTechnologyduringthela

3、st25years.”Bibliography:p.329Includesindex.1.Numbers,Theoryof.2.Arithmeticfunctions.3.Numbers,Prime.I.Title.QA24l.A6512’.7375-37697Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag.@1976bySpringer-VerlagNew

4、YorkInc.PrintedintheUnitedStatesofAmericaISBNo-387-90163-9Springer-VerlagNewYorkISBN3-540-90163-9Springer-VerlagBerlinHeidelbergivPrefaceThisisthefirstvolumeofatwo-volumetextbook’whichevolvedfromacourse(Mathematics160)offeredattheCaliforniaInstituteofTechnologyduringthe

5、last25years.Itprovidesanintroductiontoanalyticnumbertheorysuitableforundergraduateswithsomebackgroundinadvancedcalculus,butwithnopreviousknowledgeofnumbertheory.Actually,agreatdealofthebookrequiresnocalculusatallandcouldprofitablybestudiedbysophisticatedhighschoolstuden

6、ts.Numbertheoryissuchavastandrichfieldthataone-yearcoursecannotdojusticetoallitsparts.Thechoiceoftopicsincludedhereisintendedtoprovidesomevarietyandsomedepth.Problemswhichhavefascinatedgenerationsofprofessionalandamateurmathematiciansarediscussedtogetherwithsomeofthetec

7、hniquesforsc!vingthem.Oneofthegoalsofthiscoursehasbeentonurturetheintrinsicinterestthatmanyyoungmathematicsstudentsseemtohaveinnumbertheoryandtoopensomedoorsforthemtothecurrentperiodicalliterature.Ithasbeengratifyingtonotethatmanyofthestudentswhohavetakenthiscoursedurin

8、gthepast25yearshavebecomeprofessionalmathematicians,andsomehavemadenotablecontributionsoftheirowntonumbertheor