The Generalized Order of Dirichlet Series

Chen Qing-yuan; Huo Ying-ying

doi:10.12052/gdutxb.180140

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The Generalized Order of Dirichlet Series

更新时间：2026-05-27

- The Generalized Order of Dirichlet Series
- Vol. 36, Issue 4, Pages: 52-58(2019)
- 作者机构：
  
  广东工业大学　应用数学学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.180140
  CLC： O174.52
- Online First：18 June 2019，
  
  Published：2019
- 稿件说明：
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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 Qing-yuan, Huo Ying-ying. The Generalized Order of Dirichlet Series[J]. 2019, 36(4): 52-58.
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. DOI： 10.12052/gdutxb.180140.

Chen Qing-yuan, Huo Ying-ying. The Generalized Order of Dirichlet Series[J]. 2019, 36(4): 52-58. DOI： 10.12052/gdutxb.180140.

摘要

研究了全平面上Dirichlet级数的广义级. 采用Knopp-Kojima方法得到了关于Dirichlet级数的最大模和系数增长关系的结果

并在较弱的条件下将上述结果转化为Dirichlet级数的系数及其广义级的关系.

Abstract

The generalized order of Dirichlet series on the whole plane is studied. The Knopp-Kojima method is used to obtain the results of the growth relationship between the maximum modulus and the coefficients of Dirichlet series

and the above results are transformed into the relation between the coefficients of Dirichlet series and its generalized order under weak conditions.

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references

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HUO Y Y, KONG Y Y. On the generalized order of Dirichlet series [J]. Acta Mathematica Scientia, 2015, 35(1): 133-139.

KNOPP K. Über die Konvergenzabszisse des Laplace-Integrals [J]. Mathematische Zeitschrift, 1951, 54(3): 291-296.

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.

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.

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