Order of Dirichlet Series in the Whole Plane and Remainder Estimation

HUANG Hui-jun, NING Ju-hong

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

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 4: 515 - 523

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.04.004

Order of Dirichlet Series in the Whole Plane and Remainder Estimation

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

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.

Received date: 2013-09-22

Online published: 2020-11-19

Supported by

Supported by the National Natural Science Foundation of China(11171119)； Supported by the National Science Foundation of Jiangxi Province(20122BAB211005,2010GQS0103)；

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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

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

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