Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (4): 515-523.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.004

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Order of Dirichlet Series in the Whole Plane and Remainder Estimation

  

  1. 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)；

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

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

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