Geodesic
On an additive problem of number theory with random number of summands
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 1, pp. 129-150 Cet article a éte moissonné depuis la source Math-Net.Ru

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Asymptotic formulas for the mean and variance of the number of nonnegative integer solutions of the equation $x_1^m+\dots+x_s^m=N$ are obtained; here $m,s,N$ are integer positive numbers, $m=\mathrm{const}$, and $s$ is a random variable. Cases of the binomial and Poisson distributions of $s-1$ are considered. Proofs are based on the saddle point method. Analogous results for the number of nonnegative integer solutions of the inequality $x_1^m+\dots+x_s^m\le N$ are obtained also. 
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A. N. Timashev. On an additive problem of number theory with random number of summands. Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 1, pp. 129-150. http://geodesic.mathdoc.fr/item/MVK_2013_4_1_a6/

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