Geodesic
On an arithmetical method in theory of the local limit theorem for lattice distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 86-96

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Let $\xi_1,\xi_2\dots$ be a sequence of independent integer-valued variables. Sufficient conditions are given for the local limit theorem to hold. 
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     title = {On an arithmetical method in theory of the local limit theorem for lattice distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {1},
     year = {1970},
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     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a5/}
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D. A. Moskvin; L. P. Postnikova; A. A. Yudin. On an arithmetical method in theory of the local limit theorem for lattice distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 86-96. http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a5/