A Study of the Growth Results for the Hadamard Product of Several Dirichlet Series with Different Growth Indices

Hongyan Xu, Guangsheng Chen, Hari Mohan Srivastava, Hong Li, Zuxing Xuan and Yongqin Cui
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Hongyan Xu: College of Arts and Sciences, Suqian University, Suqian 223800, China
Guangsheng Chen: College of Mathematics and Computer Science, Guangxi Science & Technology Normal University, Laibin 546199, China
Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Hong Li: School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
Zuxing Xuan: Department of General Education, Beijing Union University, Beijing 100101, China
Yongqin Cui: Department of Informatics and Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China

Mathematics, 2022, vol. 10, issue 13, 1-26

Abstract: In this paper, our first purpose is to describe a class of phenomena involving the growth in the Hadamard–Kong product of several Dirichlet series with different growth indices. We prove that (i) the order of the Hadamard–Kong product series is determined by the growth in the Dirichlet series with smaller indices if these Dirichlet series have different growth indices; (ii) the q 1 -type of the Hadamard–Kong product series is equal to zero if p Dirichlet series are of q j -regular growth, and q 1 < q 2 < ⋯ < q p , q j ∈ N + , j = 1 , 2 , … , p . The second purpose is to reveal the properties of the growth in the Hadamard–Kong product series of two Dirichlet series—when one Dirichlet series is of finite order, the other is of logarithmic order, and two Dirichlet series are of finite logarithmic order—and obtain the growth relationships between the Hadamard–Kong product series and two Dirchlet series concerning the order, the logarithmic order, logarithmic type, etc. Finally, some examples are given to show that our results are best possible.

Keywords: Dirichlet series; Hadamard–Kong product; growth (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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