Relative growth of Dirichlet series with different abscissas of absolute convergence
DOI:
https://doi.org/10.37863/umzh.v72i11.6168Abstract
UDC 517.537.72
We study the growth of a Dirichlet series F(s)=∑∞n=1fnexp{sλn} with zero abscissa of absolute convergence with respect to the entire Dirichlet series G(s)=∑∞n=1gnexp{sλn} by using the generalized quantities of order ϱ0β,β[F]G=¯limσ↑0β(M−1G(MF(σ)))β(1/|σ|) and lower order λ0β,β[F]G=lim_σ↑0β(M−1G(MF(σ)))β(1/|σ|), where MF(σ)=sup M^{-1}_G(x) is the function inverse to M_G(\sigma), and \beta is a positive increasing function growing to +\infty.
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