On behaviour of integral functions represented by the Dirichlet series on the real axis

• Date: 2025
• Main Authors: Vinnitsky , В. V., Sorokivsky , V. M., Винницкий , Б. В., Сорокивский , В. М.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2025
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9367
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Conditions are found under which for an entire function $f$  represented by a Dirichlet series with finite Ritt order on some sequence $(x_k), 0<x_k↑\infty$, as $k→\infty$ one has $| f (x_k) | = M_f((1+o(1)x_k),M_f(x)=sup\{|f(z)|:{\rm Re} \ z\leq x\}$.