Geodesic
The roots of generating functions and sums of integer-valued random variables
Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 1, pp. 27-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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Properties of roots of generating functions of integer-valued bounded random variables and properties of sums of independent random variables with values in sets $\{0, 1\}$ and $\{0, 1, 2\}$ are studied. Conditions of weak convergence of integer-valued bounded random variables to the Poisson and normal laws in terms of roots of generating functions are presented. 
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A. M. Zubkov; G. I. Ivchenko; Yu. I. Medvedev. The roots of generating functions and sums of integer-valued random variables. Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 1, pp. 27-46. http://geodesic.mathdoc.fr/item/MVK_2020_11_1_a2/

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