On the growth of a klasss of Dirichlet series absolutely convergent in half-plane

Abstract

In terms of generalized orders it is investigated a relation between the growth of a Dirichlet series $F(s)=\sum\limits_{n=1}^{\infty}a_n\exp\{s\lambda_n\}$ with the abscissa of asolute convergence $A\in (-\infty,+\infty)$ and the growth of Dirichlet series $F_j(s)=\sum\limits_{n=1}^{\infty}a_{n,j}\exp\{s\lambda_n\}$, $1\le j\le 2$, with the same abscissa of absolute convergence if the coefficients $a_n$ are connected with the coefficients $a_{n,j}$ by correlation \begin{equation*} \beta\left(\dfrac{\lambda_n}{\ln\,\left(|a_n|e^{A\lambda_n}\right)}\right)=(1+o(1)) \prod\limits_{j=1}^{m}\beta\left(\dfrac{\lambda_n} {\ln\,\left(|a_{n,j}|e^{A\lambda_n}\right)}\right)^{\omega_j},\quad n\to\infty, \end{equation*} where $\omega_j>0$, $1\le j\le m$, $\sum\limits_{j=1}^{m}\omega_j=1$.

Authors and Affiliations

L. Kulyavetc', O. Mulyava

Keywords

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  • EP ID EP325065
  • DOI 10.15330/cmp.9.1.63-71
  • Views 55
  • Downloads 0

How To Cite

L. Kulyavetc', O. Mulyava (2017). On the growth of a klasss of Dirichlet series absolutely convergent in half-plane. Карпатські математичні публікації, 9(1), 63-71. https://europub.co.uk/articles/-A-325065