On the growth of a class of Dirichlet series absolutely convergent in half-plane - Kulyavetc', L.V.; Mulyava, O.M. (Carpathian Mathematical Publications, 2017)
In terms of generalized orders it is investigated a relation between the growth of a Dirichlet series F(s)=_n=1^∞a_n{sλ_n} with the abscissa of asolute convergence A(-∞,+∞) and the growth of Dirichlet series F_j(s)=_n=1^∞a_n,j{sλ_n}, 1j2, with the same abscissa of absolute convergence, if the coefficients a_n are connected with the coefficients a_n,j by correlation β(λ_n(|a_n|e^Aλ_n))=(1+o(1)) _j=1^mβ(λ_n (|a_n,j|e^Aλ_n))^ω_j, n→∞, where ω_j>0 (1jm), _j=1^mω_j=1, and α is a positive slowly increasing function on [x_0, +∞).