On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series.

For the Dirichlet series F (s) = ∑ n = 1 ∞ f n exp { s λ n } , which is the Hadamard composition of the genus m of similar Dirichlet series F j (s) with the same exponents, the growth with respect to the function G (s) given as the Dirichlet series is studied in terms of the Φ -type (the upper limit of M G − 1 (M F (σ)) / Φ (σ) as σ ↑ A ) and convergence Φ -class defined by the condition ∫ σ 0 A Φ ′ (σ) M G − 1 (M F (σ)) Φ 2 (σ) d σ < + ∞ , where M F (σ) is the maximum modulus of the function F at an imaginary line and A is the abscissa of the absolute convergence. [ABSTRACT FROM AUTHOR]

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