f_27n_f′-α的零点问题和涉与分担值的正规族

《f_27n_f′-α的零点问题和涉与分担值的正规族》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、山东大学硕士学位论文在第五章，我们利用定理I，2，分别证明了定理3，4，5和定理6．关键词：亚纯函数，正规族，分担值llI山东大学硕士学位论文ABSTRACTNormalityisimportantsubjectincomplexanalysis，manyscholarshavemadealargenumberofoutstandingcontributionstothisanddevelopedanumberofimportantresults．Inthispaperwestudythezerosofp{

2、一aandthe

3、normalityofmcromorphicfunctions．Manymathematiciansinthisareahasdonealotofdiscussionandresearch，andgotanumberofimportantconclusions．Ⅻ．K．Hayman[41]proposedaconjecturein1959：If{isatranscendentalmero-morphicfunctioninC．thenforanyn，

4、n

5、Iassumeseveryfinitenon-zerocomplexn

6、umberinfinitelyoften．Itsetoffananimateddisclmsionamongmanyworldfamousscientistsinmaths．PristlyHayman[41】himselfconfirmeditforn≥3；Further，itwasprovedbyE．Mues[42】when仡≥2．Moreover，Ha)7manprovedforentirefunctions，thisconjectureistruewhenn≥2in【46]，J．Clunie[43】provedfore

7、ntirefunction。thisconjectureistruewhen几≥1．Atlastin1995，HuaihuiChenandMingliangFang[31】ConsideredHayman’SconjectureInthecaseof竹=1，andprovedthatif，isatranscendentalmeromorphicfunctioninC。thenlltassumeseveryfinitenon-zerocomplexnumberinfinitelyoften．Y．F．Wang[30]proved

8、theconjectureOntheotherhandin1992，andgetthatif，isatranscendentalmeromorphicfunctioninC，n之3，k≥0aretwointegernumbers，then(广(z))‘a．q,sllmeseveryfinitenon-zerocomplexmmlberinfinitelyoften．MingliangFang[321133】provedthatif，isameromorphicfunc-tioninC，礼≥2isapositiveintege

9、r，bisanon-zeroconstant，if广／7≠b，thenlisaconstant；iflisatranscendentalmeromorphiefunction．thenP{

10、assumeseveryfinitenon-zerocomplexnumberinfinitelyoften．Obviously．weget：if

11、isanon-constantmeromorphicfunctionIthen铲{。一a(a≠0．圆inevitablyhaszeros．AccordingtoBlochprinciple，w

12、ecouldapplyabovetheoremstomormalfamiliesandthenobtainaseriesofnormalcriterion．Infact，somenomalcri-teriaofsuchacoursehavebeengotbyseniorscientistsinmaths．Influencedfromaboveresultsonvaluedistribution，Haymanproposedtheconjecture：歹"isanormalfamilyinD，nisafinitenon-7豫,

13、rocomplexnumber，ifforanyl∈f．{nll季吼。then≯isnormal．Itwasbccnconfirmedon80mcadditionalconditionsrespectivelybysomefanmusmathematicians．Recently,Q．C，