On certain relations between the maximum modulus and the maximal term of an entire dirichlet series

1999 ◽  
Vol 66 (2) ◽  
pp. 223-232 ◽  
Author(s):  
O. B. Skaskiv
Keyword(s):  
Dirichlet Series ◽  
Maximum Modulus ◽  
Entire Dirichlet Series ◽  
Maximal Term

scholarly journals Generalized types of the growth of Dirichlet series

2015 ◽  
Vol 7 (2) ◽  
pp. 172-187 ◽  
Author(s):  
T.Ya. Hlova ◽  
P.V. Filevych
Keyword(s):  
Dirichlet Series ◽  
Half Plane ◽  
Maximum Modulus ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Maximal Term ◽  
Necessary And Sufficient ◽  
Nonnegative Sequence

Let $A\in(-\infty,+\infty]$ and $\Phi$ be a continuously on $[\sigma_0,A)$ function such that $\Phi(\sigma)\to+\infty$ as $\sigma\to A-0$. We establish a necessary and sufficient condition on a nonnegative sequence $\lambda=(\lambda_n)$, increasing to $+\infty$, under which the equality$$\overline{\lim\limits_{\sigma\uparrow A}}\frac{\ln M(\sigma,F)}{\Phi(\sigma)}=\overline{\lim\limits_{\sigma\uparrow A}}\frac{\ln\mu(\sigma,F)}{\Phi(\sigma)},$$holds for every Dirichlet series of the form $F(s)=\sum_{n=0}^\infty a_ne^{s\lambda_n}$, $s=\sigma+it$, absolutely convergent in the half-plane ${Re}\, s<A$, where $M(\sigma,F)=\sup\{|F(s)|:{Re}\, s=\sigma\}$ and $\mu(\sigma,F)=\max\{|a_n|e^{\sigma\lambda_n}:n\ge 0\}$ are the maximum modulus and maximal term of this series respectively.

A relation between the maximal term and maximum of the modulus of the entire dirichlet series

1992 ◽  
Vol 51 (5) ◽  
pp. 522-526 ◽  
Author(s):  
M. N. Sheremeta
Keyword(s):  
Dirichlet Series ◽  
Entire Dirichlet Series ◽  
Maximal Term

scholarly journals On the maximum modulus and the coefficients of an entire Dirichlet series

1956 ◽  
Vol 8 (1) ◽  
pp. 108-113 ◽  
Author(s):  
Qazi Ibadur Rahman
Keyword(s):  
Dirichlet Series ◽  
Maximum Modulus ◽  
Entire Dirichlet Series

scholarly journals The Growth on the Maximum Modulus of Double Dirichlet Series

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yong-Qin Cui ◽  
Hong-Yan Xu ◽  
Na Li
Keyword(s):  
Dirichlet Series ◽  
Partial Derivative ◽  
Entire Functions ◽  
Maximum Modulus ◽  
Logarithmic Order ◽  
Double Dirichlet Series

The main purpose of this paper is to investigate the growth of several entire functions represented by double Dirichlet series of finite logarithmic order, h-order. Besides, we also study some properties on the maximum modulus of double Dirichlet series and its partial derivative. Our results are extension and improvement of previous results given by Huo and Liang.

On the Stability of the Maximum Term of the Entire Dirichlet Series

2005 ◽  
Vol 57 (4) ◽  
pp. 686-693
Author(s):  
O. B. Skaskiv ◽  
O. M. Trakalo
Keyword(s):  
Dirichlet Series ◽  
Maximum Term ◽  
Entire Dirichlet Series ◽  
The Stability
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