關(guān)于m次剩余數(shù)的漸近性質(zhì)和Dirichlet L-函數(shù)的加權(quán)均值.pdf

1、延安大學(xué)碩士學(xué)位論文關(guān)于m次剩余數(shù)的漸近性質(zhì)和DirichletL函數(shù)的加權(quán)均值姓名：葛丹申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：高麗20040601Onthem—PowerResiduesNumbersandtheWeightedMeanofDirichletL—FunctionsAbstract：Inthispaper，twokindsofmeanvaluearestudiedwithanalyticmethodsInchapte

2、r1，theasymptoticpropertiesofthem—powerresiduesnumbersarestudied，whichtakesthreestepsasfollowing：(1)Somepropertiesofthesquareresiduesnumbersarestudied，whichisthecaseofm=2，andfiveinterestingasymptoticformulasaregiven，(2)Tw

3、opropertiesofakindofspecialresiduesnumbers，whichisthecaseofn=po，arediscussedAndtwoasymptoticformulasareobtained，(3)SomepropertiesoftheHi—powerresiduesnumbersareproposed，andfoureor—respondingasymptoticformulasarepresented

4、Inordertoachievethegoals，firstly，someseriesaredonewhichconvergeonhalfplaneReS≥1ESecondly，theirsumscanbeexpressedasabsolutelyconvergentinfiniteproductsbyEuler’Sformula，Thirdly，expectableresultscanbeobtainedwiththePerronfo

5、rmulaandresiduetheoremandsomespecialanalyticmethodsInchapter2jbyusingtheestimateforcharactersums，theestimatefortrigonometricsumsandtheanalyticmethods，onepropertyofDirichletLfunctionswiththeweightofGausssumsarestudiedanda

6、meansquarevalueformulaisgivenatfirstThen，its2k—thmeanvalueisstudiedfurtheranditsasymptoticformulaisobtainedKeywords：ITI—powerresiduesnumbersAsymptoticpropertiesNumber—theoreticfunctionDirichletL—functionsWeightedmeanGEDa