零级和有限级Dirichlet级数和随机Dirichlet级数的增长性

数学季刊 ›› 2013, Vol. 28 ›› Issue (2): 250-256.

零级和有限级Dirichlet级数和随机Dirichlet级数的增长性

1. School of Mathematics Science, Xinjiang Normal University 2. College of Science, Shihezi University

收稿日期:2011-10-12 出版日期:2013-06-30 发布日期:2023-03-02
通讯作者: TIAN Hong-gen(1953-), male, native of Hanjiang,Jiangsu, a professor of Xinjiang Normal University, engages in teaching and studying of complex analysis and equation(corresponding author).
作者简介:YANG Qi(1979-), female, native of Akesu, Xinjiang, a lecturer of Xinjiang Normal University, engages in teaching and studying of complex analysis; TIAN Hong-gen(1953-), male, native of Hanjiang,Jiangsu, a professor of Xinjiang Normal University, engages in teaching and studying of complex analysis and equation(corresponding author).
基金资助:
Supported by the National Natural Science Foundation of China(10471048)

The Growth of Dirichlet Series and Random Dirichlet Series of Zero Order and Finite Order

1. School of Mathematics Science, Xinjiang Normal University 2. College of Science, Shihezi University

Received:2011-10-12 Online:2013-06-30 Published:2023-03-02
Contact: TIAN Hong-gen(1953-), male, native of Hanjiang,Jiangsu, a professor of Xinjiang Normal University, engages in teaching and studying of complex analysis and equation(corresponding author).
About author:YANG Qi(1979-), female, native of Akesu, Xinjiang, a lecturer of Xinjiang Normal University, engages in teaching and studying of complex analysis; TIAN Hong-gen(1953-), male, native of Hanjiang,Jiangsu, a professor of Xinjiang Normal University, engages in teaching and studying of complex analysis and equation(corresponding author).
Supported by:
Supported by the National Natural Science Foundation of China(10471048)

摘要/Abstract

摘要： In this paper, we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.

关键词: Dirichlet series, random Dirichlet series, type-function

Abstract: In this paper, we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.

Key words: Dirichlet series, random Dirichlet series, type-function

中图分类号:

O174.52

杨祺, 曹月波, 田宏根. 零级和有限级Dirichlet级数和随机Dirichlet级数的增长性[J]. 数学季刊, 2013, 28(2): 250-256.

YANG Qi, CAO Yue-bo, TIAN Hong-gen . The Growth of Dirichlet Series and Random Dirichlet Series of Zero Order and Finite Order[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(2): 250-256.

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