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| 摘要: |
| 本文研究了全平面上零级Dirichlet级数的增长性的问题.利用复级数理论，进一步讨论了在两种条件下Dirichlet级数的Dirichlet-Hadamard乘积的增长性，获得了零级Dirichlet级数及其Dirichlet-Hadamard乘积涉及对数级与对数型的几个关系定理，推广了孔荫莹等人的结果. |
| 关键词: 对数级 对数型 Dirichlet级数 Dirichlet-Hadamard乘积 |
| DOI： |
| 分类号:O174.55 |
| 基金项目:国家自然科学基金资助项目（11561033；71763013）；江西省自然科学基金项目（20151BAB201008）；江西省教育厅科技项目（GJJ160914；GJJ191603）和景德镇陶瓷大学科研资助项目. |
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| THE GROWTH AND DIRICHLET-HADAMARD PRODUCT OF DIRICHLET SERIES WITH ZERO ORDER |
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CUI Yong-qin,Zhou Feng-lin,XU Hong-yan
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| Abstract: |
| The main purpose of this paper is to investigate the growth of Dirichlet series with zero order which converges in the whole complex plane. By using the theory of complex series, we further study the growth of Dirichlet-Hadamard product of Dirichlet series with zero order under two different conditions. Some relationship theorems concerning logarithmic order and logarithmic type between Dirichlet series and its Dirichlet-Hadamard product are obtained, which are improvement and extension of previous results given by Kong. |
| Key words: logarithmic order logarithmic type Dirichlet series Dirichlet-Hadamard product |
