广东工业大学 数学与统计学院,广东,广州,510520
洪甜甜(1998–),女,硕士研究生,主要研究方向为Dirichlet级数与函数论
霍颖莹(1980–),女,副教授,博士,主要研究方向为Dirichlet级数与函数论
网络首发:2023-05-25,
纸质出版:2023
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洪甜甜, 霍颖莹. 随机Dirichlet级数在右半平面的广义逼近[J]. 广东工业大学学报, 2023, 40(3): 105-112.
Hong Tian-tian, Huo Ying-ying. Generalized Approximation of Random Dirichlet Series in the Right Half Plane[J]. 2023, 40(3): 105-112.
洪甜甜, 霍颖莹. 随机Dirichlet级数在右半平面的广义逼近[J]. 广东工业大学学报, 2023, 40(3): 105-112. DOI: 10.12052/gdutxb.210141.
Hong Tian-tian, Huo Ying-ying. Generalized Approximation of Random Dirichlet Series in the Right Half Plane[J]. 2023, 40(3): 105-112. DOI: 10.12052/gdutxb.210141.
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 $
<
img text_id='M1' class='formula-img' style='display:none;' src='gdgydxxb-40-3-105_M1.jpg'>
混合序列且满足
${({\rm{MZ}}) ^*}$
<
img text_id='M2' class='formula-img' style='display:none;' src='gdgydxxb-40-3-105_M2.jpg'>
条件的随机Dirichlet级数的广义逼近与非随机情况一致。
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 $
<
img text_id='M3' class='formula-img' style='display:none;' src='gdgydxxb-40-3-105_M3.jpg'>
mixing random variables and satisfying the
${({\rm{MZ}}) ^*}$
<
img text_id='M4' class='formula-img' style='display:none;' src='gdgydxxb-40
-3-105_M4.jpg'>
condition and obtain the relationship between the maximum modulus and the error term in approximating.
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