Geodesic
A generalization of Esseen's inequality and its application in probabilistic number theory
Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 821-844

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We prove a generalization of Esseen's inequality on rhe estimation of the difference between distribution functions in terms of the difference between their characteristic functions. The generalization holds without any restrictions on the distributions in question. The result is applied to the refinement of the limit theorems connected with the distribution of values of arithmetical functions. 
@article{IM2_1968_2_4_a8,
     author = {A. S. Fainleib},
     title = {A generalization of {Esseen's} inequality and its application in probabilistic number theory},
     journal = {Izvestiya. Mathematics },
     pages = {821--844},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a8/}
}
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A. S. Fainleib. A generalization of Esseen's inequality and its application in probabilistic number theory. Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 821-844. http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a8/