Geodesic
Some applications of Yu.~V.~Linnik's theorem on characteristic functions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 177-186

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In the paper there are given some applications of Yu. V. Linnik theorem and a result by B. Ramachandran and C. R. Rao to obtain necessary conditions for the convergence in special limit theorems. The case of convergence of sums of random number of random variables is considered too. 
@article{ZNSL_2020_495_a9,
     author = {L. B. Klebanov},
     title = {Some applications of {Yu.~V.~Linnik's} theorem on characteristic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {177--186},
     publisher = {mathdoc},
     volume = {495},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a9/}
}
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L. B. Klebanov. Some applications of Yu.~V.~Linnik's theorem on characteristic functions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 177-186. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a9/