全平面上Dirichlet级数的级与余项估计

doi:10.13371/j.cnki.chin.q.j.m.2015.04.004

数学季刊 ›› 2015, Vol. 30 ›› Issue (4): 515-523.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.004

全平面上Dirichlet级数的级与余项估计

1. Attached Primary School of Jiangxi Normal University2. College of Mathematics and Information Science, Jiangxi Normal University

收稿日期:2013-09-22 出版日期:2015-12-30 发布日期:2020-11-19
作者简介:HUANG Hui-jun(1989-), female, native of Jian, Jiangxi, a teacher of Attached Primary School of Jiangxi Normal University, engages in studying of complex analysis; NING Ju-hong(correspording author)(1977-), female, native of Sanmenxia, Henan, an associate professor of Jiangxi Normal University, engages in studying of complex analysis.
基金资助:
Supported by the National Natural Science Foundation of China(11171119)； Supported by the National Science Foundation of Jiangxi Province(20122BAB211005,2010GQS0103)；

Order of Dirichlet Series in the Whole Plane and Remainder Estimation

1. Attached Primary School of Jiangxi Normal University2. College of Mathematics and Information Science, Jiangxi Normal University

Received:2013-09-22 Online:2015-12-30 Published:2020-11-19
About author:HUANG Hui-jun(1989-), female, native of Jian, Jiangxi, a teacher of Attached Primary School of Jiangxi Normal University, engages in studying of complex analysis; NING Ju-hong(correspording author)(1977-), female, native of Sanmenxia, Henan, an associate professor of Jiangxi Normal University, engages in studying of complex analysis.
Supported by:
Supported by the National Natural Science Foundation of China(11171119)； Supported by the National Science Foundation of Jiangxi Province(20122BAB211005,2010GQS0103)；

摘要/Abstract

摘要： In this paper, firstly, the ρ order and ρ_βorder of Dirichlet series which converges in the whole plane are studied. Secondly, the equivalence relation between remainder logarithm ln E_n-1（f, α）, ln R_n（f, α） and coefficients logarithm ln |a_n| is discussed respectively. Finally,the theory of applying remainder to estimate ρ order and ρ_βorder can be obtained by using the equivalence relation.

关键词: Dirichlet series, ρ order, ρ_βorder, remainder estimation

Abstract: In this paper, firstly, the ρ order and ρ_βorder of Dirichlet series which converges in the whole plane are studied. Secondly, the equivalence relation between remainder logarithm ln E_n-1（f, α）, ln R_n（f, α） and coefficients logarithm ln |a_n| is discussed respectively. Finally,the theory of applying remainder to estimate ρ order and ρ_βorder can be obtained by using the equivalence relation.

Key words: Dirichlet series; ρ order; ρ_βorder, remainder estimation

中图分类号:

O173

黄慧珺, 宁菊红. 全平面上Dirichlet级数的级与余项估计[J]. 数学季刊, 2015, 30(4): 515-523.

HUANG Hui-jun, NING Ju-hong. Order of Dirichlet Series in the Whole Plane and Remainder Estimation[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(4): 515-523.

[1]	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.
[2]	丁晓庆, 刘薇. 零级数Dirichlet级数的增长性[J]. 数学季刊, 2010, 25(2): 282-286.
[3]	田宏根, 孙道椿. 右半平面上的零级Dirichlet 级数的增长性 [J]. 数学季刊, 2007, 22(4): 512-517.

全平面上Dirichlet级数的级与余项估计

Order of Dirichlet Series in the Whole Plane and Remainder Estimation

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