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; +∞).
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Vynnyts'kyi, B.V., Sharan, V.L. On Zeros of One Class of Functions Analytic in a Half-Plane. Ukrainian Mathematical Journal 55, 1514–1521 (2003). https://doi.org/10.1023/B:UKMA.0000018012.05724.a2
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DOI: https://doi.org/10.1023/B:UKMA.0000018012.05724.a2