On the Stability of the Maximum Term of the Entire Dirichlet Series

• Date: 2005
• Main Authors: Skaskiv, O. B., Trakalo, O. M., Скасків, О. Б., Тракало, О. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3623
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish necessary and sufficient conditions for logarithms of the maximal terms of the entire Dirichlet series $F(z) = \sum^{+\infty}_{n=0}a_n e^{z\lambda_n}$ and $A(z) = \sum^{+\infty}_{n=0}a_n b_n e^{z\lambda_n}$ to be asymptotically equivalent as ${\rm Re}\;z \rightarrow +\infty$ outside s...