On Zeros of One Class of Functions Analytic in a Half-Plane

Abstract

We describe sequences of zeros of functions f ≢ 0 analytic in the half-plane ${\mathbb{C}}_ + = \{ z:\operatorname{Re} z >0\}$ and satisfying the condition $(\exists {\tau}_1 \in (0;1))(\exists c_1 >0)(\forall z \in {\mathbb{C}}_ + ):|f(z)| \leqslant c_1 \exp ({\eta}^{\tau }_1 (c_1 |z|)),$ where η: [0; +∞) → (0; +∞) is an increasing function such that the function ln η(r) is convex with respect to ln r on [1; +∞).