简介：为任意的给定的积极条款系列$\sum\limits_{k=1}^\infty{a_k}$并且$\sum\limits_{k=1}^\infty{b_k}$，现在的纸为$\mathop提供一个有趣的必要、足够的条件{啜}\limits_{n\geqslant1}\{\sum\limits_{k=1}^n{a_k/\sum\limits_{k=1}^n{b_k}}\}=\infty$。

简介：为在上可辨的功能(0，1)有检验了某三角法的系列(1)的工具(2)。节2包含一些基本估计。在节3，作者介绍二条主要定理，它对应于提议1，中的2个[3]。

简介：SubmissionPleasetypeyourpaperinLaTeX,ande-mailthepdffile.Theeditorialofficewillconfirmreceiptwithin3days.Ifyoudonotreceivethereceiptletter,pleasesendane-mailtoask.TheaddressisEditorialBoard,ActaMathematicaSinica(EnglishSeries),InstituteofMathematics,AcademiaSinica,Zhongguancun,Beijing100080,China,email:syc@amss.ac.cn.

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简介：ThisarticleinvestigatestheconvergenceandgrowthofmultipleDirichletseries.TheValironformulaofDirichletseriesisextendedton-tupleDirichletseriesandanequivalencerelationbetweentheorderofn-tupleDirichletseriesanditscoefficientsandexponentsisobtained.

简介：<正>InstructionstoAuthorsSubmissionTypescriptsshouldbesubmittedinduplicatetotheEditorialBoardofActaMathematicaSinica(NewSeries),InstituteofMathematics,CAS,Beijing100080,China.TypescriptsshouldbetypedinEnglish,doublespacedandsingle-sidedonA-4sheetsandshouldbenumberedbeginningwiththetitlepage.Thefirstpageofanarticleshouldcontainonly(1)thetitleofthepaper,thename(s)

简介：<正>InthepresentnotethealgebraicindependenceofvaluesofseveralMahlerserieswithcertainparticularanddifferentparametersatalgebraicpointsisestablishedbymeansofatypicalapproximationmethodhandlingtheLiouvilletypeseries.

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简介：Inthispaper,wefirstdiscussthemethodsofcomparingtwospecialabsolutelyconvergentsineseries,sinnxandsinnx.Westatethetheoremin.onedimensionalcaseasfollows;Theorem.Letbeconvergentserieswithnonnegativeterms.SupposeThenforallx∈[0,π]If,inaddition,then

简介：现在的纸建议一个新自然弱条件代替thequasimonotone和O定期变化的伪单调条件，并且显示出主要结果的结论在[10]静止抓住。而且，我们证明任何O定期变化的伪单调条件暗示这个条件，这样tnequasimonotonicity的含糊的牵连能在实践被避免。

简介：LetXbeaBanachspaceand{ej}j=1beasequenceinX.Theauthorshowse∞that{ej}∞j+1isabasicsequenceifandonlyif∑n∞=1rnαnjconvergesforeveryj＞1ande∞-∞∞e∑∞n=1rn∑∞j=1αnjej=∑j=1(∑∞n=1rnαnj)jholdsforeverychoiceofscalarvariables{αnj}suchthat∑∞n=1αnjejconvergesforeachn>-1andanychoiceofscalarvariables{rn}suchthat∑∞n+1∑∞f=1rnαnjejconverges.Moreover,someapplicationsabouttheresultaregiven.

简介：Let{X,Xn,n≥1}beasequenceofi.i.d.randomvariableswithzeromean,andsetSn=Σk=1nXk,EX2=σ2>0,λ(ε)=Σn=1∞P(|Sn|≥nε).Inthispaper,wediscusstherateoftheapproximationofσ2byε2λ(ε)undersuitableconditions,andimprovethecorrespondingresultsofKlesov(1994).

简介：在这篇文章，Dirichlet系列的唯一定理被证明。然后在权利的随机的Dirichlet系列半飞机被学习，并且有限顺序的随机的Dirichlet系列几乎肯定有的结果(a.s)没有缺乏的功能被证明。给词调音：随机的系列；Dirichlet系列；缺乏的多项式；价值分发

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简介：ThepurposeofthispaperistostudythepointwiseandalmosteverywhereconvergenceoftheCesaromeans(C,δ)ofFourier-Jacobiexpansions,themaintermoftheLebesgueconstantofthe(C,8)meansfor-1<δ≤α+1/2isobtained.WiththeaidofthegeneralizedtranslationintermsofJacobipolynomials,pointwiseconvergencetheoremsofthe(C,δ)meansforδ>α+1/2andequiconvergencetheoremsfor-1<δ≤α+1/2areproved.TheanaloguesoftheLebesgue,SalemandYoungtheoremsoftheCesaromeansatthecriticalindexδ=α+1/2areestablished.

简介：Supposethat{Xn（ω）}areindependentrandomcomplexvariablesequence,E（Xn）-0andThenthecircle{|Z|=ρ}isalmostsurelyanaturalboundaryoftherandomseriessumfromn=1to∞Xn（ω）Zn-1

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