Generalized types of the growth of Dirichlet series
Let A(-∞,+∞] and Φ be a continuously on [σ_0,A) function such that Φ(σ)→+∞ as σ→ A-0. We establish a necessary and sufficient condition on a nonnegative sequence λ=(λ_n), increasing to +∞, under which the equality _σA M(σ,F)Φ(σ)=_σA μ(σ,F)Φ(σ), holds for every Dirichlet series of the form F(s)=_n=0^∞ a_ne^sλ_n, s=σ+it, absolutely convergent in the half-plane Re s<A, where M(σ,F)={|F(s)|:Re s=σ} and μ(σ,F)={|a_n|e^σλ_n:n0} are the maximum modulus and maximal term of this series respectively. , number=2, journal=Carpathian Mathematical Publications, author=Hlova, T.Ya. and Filevych, P.V., year=2015, month=Dec., pages=172–187