A study of the growth results for the Hadamard product of several Dirichlet series with different growth indices
Date
2022
Authors
Xu, Hongyan
Chen, Guangsheng
Srivastava, H.M.
Li, Hong
Xuan, Zuxing
Cui, Yongqin
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
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 q1-type of
the Hadamard–Kong product series is equal to zero if p Dirichlet series are of qj-regular growth, and
q1 < q2 < . . . < qp, qj ∈ 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.
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Citation
Xu, H., Chen, G., Srivastava, H., Li, H., Xuan, Z., & Cui, Y. (2022). “A study of the growth results for the Hadamard product of several Dirichlet series with different growth indices.” Mathematics, 10(13), 2220. https://doi.org/10.3390/math10132220