| 新Dirichlet级数Σn=0∞aneλns收敛横坐标 |
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| 引用本文： | 孔荫莹,罗茜.新Dirichlet级数Σn=0∞aneλns收敛横坐标[J].数学学报,2018,61(2):347-352. |
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| 作者姓名： | 孔荫莹 罗茜 |
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| 作者单位： | 1. 广东财经大学统计与数学学院 广州 510320;
2. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204, USA;
3. 嘉应学院数学学院 梅州 514015 |
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| 基金项目： | 广东省自然科学基金（2015A030313628）及省高等学校优秀青年教师培养计划（Yqgdufe1405）；国家高等教育质量常态监测数据中心（广州）开放基金（G1613）；国家留学基金（201608440448）} |
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| 摘 要： | 本文给出新Dirichlet级数Σn=0∞aneλns的收敛横坐标σc、一致收敛横坐标σu和绝对收敛横坐标σa的定义.通过指数λn和系数an的关系去估计三个横坐标，并补充证明两类Dirichlet级数Σn=0∞aneλns和Σn=0∞ane-λns的收敛条件是一致的.
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The Abscissa of Convergence on the Dirichlet Series Σn=0∞aneλns |
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| Yin Ying KONG,Xi LUO.The Abscissa of Convergence on the Dirichlet Series Σn=0∞aneλns[J].Acta Mathematica Sinica,2018,61(2):347-352. |
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| Authors: | Yin Ying KONG Xi LUO |
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| Institution: | 1. Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China;
2. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204, USA;
3. School of Mathematics, Jiaying University, Meizhou 514015, P. R. China |
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| Abstract: | We define the abscissa of convergence σc, the uniform abscissa of convergence σu and the absolute abscissa of convergence σa on Dirichlet series Σn=0∞ aneλns,use the relationship between the index λn and the coefficients an to estimate the three convergence abscissas, and obtain that the convergence conditions of two Dirichlet series Σn=0∞ aneλns and Σn=0∞ ane-λns are the same. |
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| Keywords: | Dirichlet series abscissa of convergence Abel-Stolz theorem |
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