THE GROWTH OF DIRICHLET SERIES ABSOLUTELY CONVERGENT IN A HALF-PLANE IN TERMS OF GENERALIZED TYPES
LetA(−∞,+∞). We establish a necessary and sufficient condition on a nonnegative sequence (λ_n), increasing to +∞, under which there exists a function Φ, convex and increasing to +∞ on (-∞,A), such that for every Dirichlet series of the form F(s) =a_n e^sλ_n, s =σ+it, absolutely convergent in the half-plane Re s<A we have _σA{|F(s)|: Re s = σ Φ(σ)=_σA {|a_n|e^σλ_n: n0 Φ(σ). , number=1(33), journal=PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, author=Глова, Тарас Ярославович, year=2019, month=Feb., pages=103–109