1、山東大學碩士學位論文能表為一個素數和兩個素數平方和的整數分布姓名：劉文劍申請學位級別：碩士專業(yè)：基礎數學指導教師：展?jié)齽⒔▉?0070519山東大學碩士學位論文DISTRIBUTIoNoFINTEGERSTHATARESUMSoFAPRIMEANDTWOSQUARESoFPRIMESWenjianLiu(SchoolofMathematicsandSystemSciences，ShandongUniversity)(Jinan25010

2、0，PRChina)Email：wjliuQmailsdueducnAbstractInthispaperweprovethatwithatmost0(Ⅳ備5)exceptions，allpositiveintegers幾≤NsatisfyingsomenecessarycongruenceconditionsarethesumofaprimeandtwosquaresofprimesThisimprovessubstantiallyt

3、hepreviousresultsinthisdirectionUsuallywejustusethecirclemethodtodealwithmanyadditiveprimeproblemsincludingtheoneinthispaperThereisalwaysavitalobstacleinourresearch，thatis，theestimatesofexponentialsumsinminorarcsIfweonly

4、usethecirclemethod，wehadbetterusetheestimatesofAGhoshandXiuminRen，butthiscandothelimitedimprovementtoourproblemHerewewillcombinethecirclemethodwiththesievemethod，developedbyGHarmanandAVKumchevByintroducingP，anontriviallo

5、werboundforthecharacteristicfunctionofthesetofprimes，withmanynecessaryproperties，wecanimprovetheestimateinminorarcssothatthebetterresultwillbeobtainedKeywords：circlemethod，sievemethod，Cauchy’SinequalityDirichletcharactes