On an estimation of R-type of entire Dirichlet series and its exactness
Let (λ_n) be a nonnegative sequence, increasing to +∞, τ=_n→∞nλ_n, and ρ be a positive number. It follows from a classical theorem of G. Valiron that for every Dirichlet series of the form F(s)=a_ne^sλ_n we have _σ→+∞{|F(s)|: Re s=σ e^ρσ e^ρτ _n→∞λ_neρ|a_n|^ρλ_n. The exactness of this estimation is proved in the paper. , number=2, journal=Carpathian Mathematical Publications, author=Hlova, T.Ya. and Filevych, P.V., year=2013, month=Dec., pages=208–216