Geodesic
A~generalization of Marcinkiewich's theorem on integer characteristic functions of probability distributions
Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 94-103

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The result of the paper is the following one: Let the function $\varphi(z)$ be analitic and of finite order $\rho>0$ in the upper half-plane. Suppose the function $\varphi(z)$ has no zeros and satisfies the following condition: $|\varphi(z)|\leq\varphi(i\operatorname{Im}z)$. Than $\rho\leq3$. 
@article{ZNSL_1979_85_a6,
     author = {I. P. Kamynin},
     title = {A~generalization of {Marcinkiewich's} theorem on integer characteristic functions of probability distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--103},
     publisher = {mathdoc},
     volume = {85},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a6/}
}
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I. P. Kamynin. A~generalization of Marcinkiewich's theorem on integer characteristic functions of probability distributions. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 94-103. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a6/