On conditions for Dirichlet series absolutely convergent in a half-plane to belong to the class of convergence

• Date: 2008
• Main Authors: Mulyava, O. M., Sheremeta, M. M., Мулява, О. М., Шеремета, М. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3202
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For a Dirichlet series $F(s) = \sum^{\infty}_{n=0}a_n \exp \{s\lambda_n\}$ with the abscissa of absolute convergence $\sigma_a = 0$, let $M(\sigma) = \sup\{|F(\sigma+it)|:\;t \in {\mathbb R}\}$ and $\mu(\sigma) = \max\{|a_n| \exp(\sigma \lambda_n):\;n \geq 0\},\quad \sigma < 0.$ It is prov...