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On zeros of functions of given proximate formal order analytic in a half-plane
Authors:B V Vinnitskii  V L Sharan
Abstract:We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition

$$\forall \varepsilon  > 0\exists c_1  \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma  + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$
where 0≤σ<+∞ and η is a positive function continuously differentiable on 0; +∞) and such thatxη′(x)/η(x)→0 asx→+∞. Drohobych Pedagogic University, Drohobych. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 904–909, July, 1999.
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