Journal of Guangdong University of Technology ›› 2023, Vol. 40 ›› Issue (03): 105-112.doi: 10.12052/gdutxb.210141

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Generalized Approximation of Random Dirichlet Series in the Right Half Plane

Hong Tian-tian, Huo Ying-ying   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520 China
  • Received:2021-09-27 Online:2023-05-25 Published:2023-06-08

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Abstract: By introducing the concept of generalized order and type, and using Newton polygon, a study is conducted on the random Dirichlet series in the right half plane whose coefficients are $\varphi $ mixing random variables and satisfying the ${({\rm{MZ}}) ^*}$ condition and obtain the relationship between the maximum modulus and the error term in approximating.

Key words: $\varphi $ mixing, random Dirichlet series, error, generalized order, generalized type

CLC Number: 

  • O174.52
[1] 余家荣, 丁晓庆, 田范基. Dirichlet级数与随机Dirichlet级数的值分布 [M]. 武汉: 武汉大学出版社, 2004.
[2] 陈青远, 霍颖莹. Dirichlet级数的广义级[J]. 广东工业大学学报, 2019, 36(4): 52-58.
CHEN Q Y, HUO Y Y. The generalized order of Dirichlet series [J]. Journal of Guangdong University of Technology, 2019, 36(4): 52-58.
[3] 应锐, 崔永琴, 徐洪焱. 半平面上Dirichlet级数的广义级与逼近[J]. 数学的实践与认识, 2020, 50(12): 210-219.
YING R, CUI Y Q, XU H Y. The generalizes order and approximation of Dirichlet series converges in the half plane [J]. Mathematics in Practice and Theory, 2020, 50(12): 210-219.
[4] 毕家烨, 霍颖莹. 多重Laplace-Stieltjes变换的两个等式[J]. 广东工业大学学报, 2021, 38(1): 82-88.
BI J Y, HUO Y Y. Two equalities of multiple Laplace-Stieltjes transform [J]. Journal of Guangdong University of Technology, 2021, 38(1): 82-88.
[5] KONG Y Y, GAN H L. On orders and types of Dirichlet series of slow growth [J]. Turkish Journal of Mathematics, 2010, 34(1): 1-11.
[6] 徐洪焱, 易才凤. 半平面上有限级Dirichlet级数的逼近[J]. 数学学报, 2010, 53A(3): 617-624.
XU H Y, YI C F. The approximation problem of Dirichlet series of finite order in the half plane [J]. Acta Mathematica Sinica, 2010, 53A(3): 617-624.
[7] YU J R. Some properties of random Dirichlet series [J]. Acta Mathematica Sinica, 1978, 21A(2): 97-118.
[8] DING X Q, XIAO Y M. Natural boundary of random Dirichlet series [J]. Ukrainian Mathematical Journal, 2006, 58(7): 997-1005.
[9] 孔荫莹, 霍颖莹. 慢增长的随机Dirichlet级数[J]. 数学年刊, 2012, 33A(3): 323-328.
KONG Y Y, HUO Y Y. The random Dirichlet series with slow growth [J]. Chinese Annals of Mathematics, 2012, 33A(3): 323-328.
[10] IBRAGIMOV I A. Some limit theorems for stochastic processes stationary in the strict sense [J]. Doklady Akademii Nauk SSSR, 1959, 125(4): 711-714.
[11] COGBURN R. Asymptotic properties of stationary sequences [M]. California: University of California, 1960.
[12] HUO Y Y, KONG Y Y. On generalized orders and generalized types of Dirichlet series in the right half-plane [J]. Acta Mathematica Scientia, 2014, 34B(1): 175-182.
[13] GUNDY R F. The martingale version of a theorem of Marcinkiewicz and Zygmund [J]. The Annals of Mathematical Statistics, 1967, 38(3): 725-734.
[14] 王辉坚, 孙道椿. B-值双随机Dirichlet 级数[J]. 数学物理学报, 2010, 30A(6): 1604-1611.
WANG H J, SUN D C. B-valued Bi-random Dirichlet series [J]. Acta Mathematica Scientia, 2010, 30A(6): 1604-1611.
[15] 宁菊红, 朱丽荣, 黄文平. Dirichlet级数余项在右半平面的广义级和广义型[J]. 数学的实践与认识, 2020, 50(17): 162-168.
NING J H, ZHU L R, HUANG W P. Generalized order and generalized type of the remainder of Dirichlet series in the right half plane [J]. Mathematics in Practice and Theory, 2020, 50(17): 162-168.
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