广东工业大学学报 ›› 2023, Vol. 40 ›› Issue (03): 105-112.doi: 10.12052/gdutxb.210141

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随机Dirichlet级数在右半平面的广义逼近

洪甜甜, 霍颖莹   

  1. 广东工业大学 数学与统计学院, 广东 广州 510520
  • 收稿日期:2021-09-27 出版日期:2023-05-25 发布日期:2023-06-08
  • 通信作者: 霍颖莹(1980-),女,副教授,博士,主要研究方向为Dirichlet级数与函数论。E-mail:huoyingy@gdut.edu.cn
  • 作者简介:洪甜甜(1998-),女,硕士研究生,主要研究方向为Dirichlet级数与函数论
  • 基金资助:
    国家自然科学基金资助项目(11501127)

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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摘要： 通过引入广义级和广义型的概念，利用Newton多边形，研究了半平面上用多项式逼近随机Dirichlet级数时所产生的偏差与最大模的关系，证明了系数是$\varphi $混合序列且满足${({\rm{MZ}}) ^*}$条件的随机Dirichlet级数的广义逼近与非随机情况一致。

关键词: $\varphi $混合, 随机Dirichlet级数, 偏差, 广义级, 广义型

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

中图分类号: 

  • O174.52
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