Relative growth of Dirichlet series with different abscissas of absolute convergence - Mulyava, O. M.; Sheremeta , M. M. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 517.537.72 We study the growth of a Dirichlet series F(s)=_n=1^∞f_n{sλ_n} with zero abscissa of absolute convergence with respect to the entire Dirichlet series G(s)=_n=1^∞g_n{sλ_n} by using the generalized quantities of order ρ^0_β,β[F]_G=olimits_σ0β(M^-1_G(M_F(σ)))β(1/|σ|) and lower order λ^0_β,β[F]_G=_σ0 β(M^-1_G(M_F(σ)))β(1/|σ|), where M_F(σ)={|F(σ+it)|tR}, M^-1_G(x) is the function inverse to M_G(σ), and β is a positive increasing function growing to +∞.