Generalized and modified orders of growth for Dirichlet series absolutely convergent in a half-plane
P. V. Filevych,
O. B. Hrybel
Abstract:Let $\lambda=(\lambda_n)_{n\in\mathbb{N}_0}$ be a non-negative sequence increasing to $+\infty$, $\tau(\lambda)=\varlimsup_{n\to\infty}(\ln n/\lambda_n)$, and $\mathcal{D}_0(\lambda) $ be the class of all Dirichlet series of the form $F(s)=\sum_{n=0}^\infty a_n(F)e^{s\lambda_n}$ absolutely convergent in the half-plane $\operatorname{Re}s<0$ with $a_n(F)\not=0$ for at least one integer $n\ge0$. Also, let $\alpha$ be a continuous function on $[x_0,+\infty)$ increasing to $+\infty$, $\beta$ be a continuous fun… Show more
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