The growth of the maximal term of Dirichlet series
Let Λ be the class of nonnegative sequences (λ_n) increasing to +∞, A(-∞,+∞], L_A be the class of continuous functions increasing to +∞ on [A_0,A), (λ_n)Λ, and F(s)=a_ne^sλ_n be a Dirichlet series such that its maximum term μ(σ,F)=_n|a_n|e^σλ_n is defined for every σ(-∞,A). It is proved that for all functions αL_+∞ and βL_A the equalityρ^*_α,β(F)=_(η_n)Λ_n→∞ α(η_n)β(η_nλ_n+1λ_n1|a_n|) holds, where ρ^*_α,β(F) is the generalized α,β-order of the function μ(σ,F), i.e. ρ^*_α,β(F)=0 if the function μ(σ,F) is bounded on (-∞,A), and ρ^*_α,β(F)=_σA α(μ(σ,F))/β(σ) if the function μ(σ,F) is unbounded on (-∞,A). , number=1, journal=Carpathian Mathematical Publications, author=Filevych, P.V. and Hrybel, O.B., year=2018, month=Jul., pages=79–81