Generalized types of the growth of Dirichlet series
Journal Title: Карпатські математичні публікації - Year 2015, Vol 7, Issue 2
Abstract
Let A∈(−∞,+∞] and Φ be a continuously on [σ0,A) function such that Φ(σ)→+∞ as σ→A−0. We establish a necessary and sufficient condition on a nonnegative sequence λ=(λn), increasing to +∞, under which the equality ¯¯¯¯¯¯¯¯limσ↑AlnM(σ,F)Φ(σ)=¯¯¯¯¯¯¯¯limσ↑Alnμ(σ,F)Φ(σ), holds for every Dirichlet series of the form F(s)=∑∞n=0anesλn, s=σ+it, absolutely convergent in the half-plane Res<A, where M(σ,F)=sup{|F(s)|:Res=σ} and μ(σ,F)=max{|an|eσλn:n≥0} are the maximum modulus and maximal term of this series respectively.
Authors and Affiliations
T. Ya. Hlova, P. V. Filevych
Keywords
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