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Dirichlet级数的Dirichlet-Hadamard乘积
引用本文:孔荫莹,邓冠铁.Dirichlet级数的Dirichlet-Hadamard乘积[J].数学年刊A辑(中文版),2014,35(2):145-152.
作者姓名:孔荫莹  邓冠铁
作者单位:广东财经大学数学与统计学院, 广州 510320.;北京师范大学数学科学学院, 北京 100875.
基金项目:国家自然科学基金 (No.11101096, No.11301140, No.11271045)和广东省自然科学基金 (No.S2012010010376)
摘    要:作者构造一个由两个 Dirichlet级数组成的Dirichlet-Hadamard乘积, 得到它的(下)$q$-\!\!级和(下)$q$-\!\!型的上界或下界的估计定理, 并证明了在一定条件下所得的Dirichlet-Hadamard乘积是完全正规增长的, 并把相应结果推广到乘积函数的线性代换中.

关 键 词:Dirichlet-Hadamard乘积    (下)$q$-\!\!级    (下)$q$-\!\!型    完全正规增长

The Dirichlet-Hadamard Product of Dirichlet Series
KONG Yinying and DENG Guantie.The Dirichlet-Hadamard Product of Dirichlet Series[J].Chinese Annals of Mathematics,2014,35(2):145-152.
Authors:KONG Yinying and DENG Guantie
Institution:School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China.;School of Mathematical Science, Beijing Normal University, Beijing 100875, China.
Abstract:The present paper concerns with some estimates on the upper and the lower bounds of the (lower) $q$-order and the (lower) $q$-type of a new product function defined by two Dirichlet series, named the Dirichlet-Hadamard product. This product is of regular growth or perfectly regular growth, when two constituent Dirichlet series satisfy some special conditions. Finally, we generalize a result to the subject of linear substitution.
Keywords:Dirichlet-Hadamard product    (Lower) $q$-order  (Lower) $q$-type    Perfectly  regular growth
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