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| 摘要: |
| 本文研究了半平面上零级Dirichlet级数的增长性和正规增长性.利用型函数,得到了其系数与增长性之间关系的两个充要条件,并证明了当随机变量序列{Xn(ω)}满足一定条件时,零级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同. |
| 关键词: Dirichlet级数 随机Dirichlet级数 型函数 增长性 |
| DOI： |
| 分类号:O174.52 |
| 基金项目:国家自然科学基金资助(10471048). |
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| THE GROWTH OF THE DIRICHLET SERIES AND RANDOM DIRICHLET SERIES OF ZERO ORDER IN THE HALF PLANE |
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CHEN Wei,YANG Qi,TIAN Hong-gen
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| Abstract: |
| In this paper, the growth and regular growth of Dirichlet series of zero order in the half plane are studied. By using type-function, two necessary and sufficient conditions about the relation between coefficients and growth of the Diriehlet series are obtained. We also prove that, when the random variable sequence {Xn(ω)} meets certain condition, the growth of random entire functions defined by random Dirichlet series of zero order in any horizontal straight line is almost surely equal to the growth of entire functions defined by their corresponding Dirichlet series. |
| Key words: Dirichlet series random Dirichlet series type function growth |
