On the growth of a klasss of Dirichlet series absolutely convergent in half-plane
Journal Title: Карпатські математичні публікації - Year 2017, Vol 9, Issue 1
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 69
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