| 无限级Dirichlet级数及随机Dirichlet级数 |
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| 引用本文： | 高宗升.无限级Dirichlet级数及随机Dirichlet级数[J].系统科学与数学,2000,20(2):187-195. |
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| 作者姓名： | 高宗升 |
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| 作者单位： | 北京航空航天大学应用数学系!北京 100083 |
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| 基金项目： | 国家自然科学基金，北航理学院基金 |
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| 摘 要： | 主要研究全平面上无限级Ｄｉｒｉｃｈｌｅｔ级数及随机Ｄｉｒｉｃｈｌｅｔ级数的增长性．对于 Ｄｉｒｉｃｈｌｅｔ级数，研究了它的增长性和正则增长性，得到了它的系数和指数与增长级的两 个充要条件．对于随机Ｄｉｒｉｃｈｌｅｔ级数，证明了它的增长性几乎必然与其在每条水平直线 上的增长性相同．
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| 关 键 词： | Dirichlet 级数 随机Dirichlet级数 增长性. |
THE DIRICHLET SERIES AND RANDOM DIRICHLET SERIES OF INFINITE ORDER |
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| Zong Sheng GAO.THE DIRICHLET SERIES AND RANDOM DIRICHLET SERIES OF INFINITE ORDER[J].Journal of Systems Science and Mathematical Sciences,2000,20(2):187-195. |
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| Authors: | Zong Sheng GAO |
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| Institution: | Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083,P.R.China |
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| Abstract: | in this papers we investigate the growth of Dirichlet series of infinite order in the plane; we first obtain two necessary and sufficient conditions of this Dirichlet series, and then prove that the growth of random entire functions defined by random Dirichlet series of infinite order in every horizontal straight line is almost surely equal to the growth of entire functions defined by their corresponding Dirichlet series. |
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| Keywords: | Dirichlet series random Dirichlet series growth |
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