Geodesic
On the closeness of distribution of some random variable to the equiprobable one
Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 1, pp. 5-14 
V. A. Vatutin. On the closeness of distribution of some random variable to the equiprobable one. Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 1, pp. 5-14. http://geodesic.mathdoc.fr/item/MVK_2023_14_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $b \geqslant 2$ and $N$ be natural numbers, $X_0,X_1,\ldots ,X_{n-1}$ be nonhomogeneous sequence of independent random variables taking values $0, 1,\ldots , b-1$, $$Y_{n}=X_{0}+bX_{1}+\ldots+X_{n-2}b^{n-2}+X_{n-1}b^{n-1}$$ and $$Z_{n}=Y_{n}\text{ mod }N.$$ We estimate the closeness of distribution of random variable $Z_n$ to the uniform distribution on $\{0,1,\ldots,N-1\}$ in the case when $b$ and $N$ are mutually prime.

[1] Malyshev F. M., “Modelirovanie ravnomernogo raspredeleniya, ustoichivoe k neravnoveroyatnosti iskhodnykh znakov”, Diskretnaya matematika, 17:4 (2005), 72–80 | DOI | MR | Zbl

[2] Neumann J. von, “Various techniques used in connection with random digits”: John von Neumann, Collected Works, v. V, MacMillan, New York, 1963, 768–770 | MR