| Abstrakt: |
Let A ∈ (−∞, +∞], Φ : [a, A) → R be a continuous function such that xσ − Φ(σ) → −∞ as σ ↑ A for every x ∈ R, Φe (x) = max{xσ − Φ(σ) : σ ∈ [a, A)} be the Young-conjugate function of Φ, Φ(x) = Φe (x)/x and Γ(x) = (Φe(x) − ln x)/x for all sufficiently large x, (λn) be a nonnegative sequence increasing to +∞, and F(s) = ∞ ∑ n=0 ane sλn be a Dirichlet series such that its maximal term µ(σ, F) = max{|an|e σλn : n ≥ 0} and central index ν(σ, F) = max{n ≥ 0 : |an|e σλn = µ(σ, F)} are defined for all σ < A. It is proved that if ln µ(σ, F) ≤ (1 + o(1))Φ(σ) as σ ↑ A, then the inequalities lim σ↑A µ(σ, F ′ ) /µ(σ, F)Φ −1(σ) ≤ 1, lim σ↑A λν(σ,F ′) Γ−1(σ) ≤ 1, hold, and these inequalities are sharp. [ABSTRACT FROM AUTHOR] |
